Alternating groups (and variants)

Alternating groups and their variants

Alternating group	Variants
$\mathrm{A}_{4}$	$\mathrm{S}_{4}$
$\mathrm{A}_{5}$	$\mathrm{S}_{5}$	$\mathrm{SL}_2(5)$
$\mathrm{A}_{6}$	$\mathrm{S}_{6}$	$\mathrm{PGL}_2(9)$	$\mathrm{M}_{10} = \mathrm{A}_6.2_3$	$\mathrm{Aut}(\mathrm{A}_6) = \mathrm{A}_6.2^2$	$\mathrm{SL}_2(9)$
$\mathrm{A}_{7}$	$\mathrm{S}_{7}$
$\mathrm{A}_{8}$	$\mathrm{S}_{8}$
$\mathrm{A}_{9}$	$\mathrm{S}_{9}$
$\mathrm{A}_{10}$	$\mathrm{S}_{10}$
$\mathrm{A}_{11}$	$\mathrm{S}_{11}$
$\mathrm{A}_{12}$
$\mathrm{A}_{13}$

Alternating groups in more detail

Group	Standard generators	Conjugacy classes	Character information	Modular information	Permutation representations	Linear representations	Maximal subgroups
$\text{A}_\text{5}$	Yes	Yes	Complete	Complete	All primitive	All irreducibles in all characteristics	All, with SLPs with standard generators if applicable
$\text{A}_\text{6}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{7}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{8}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{9}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{10}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{11}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{12}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{A}_\text{13}$	Yes	Yes	Complete	No Ext matrix for characteristics 2,3	All primitive up to 500000 points	All irreducible in positive characteristic up to dimension 4000	All, with SLPs with standard generators if applicable

Symmetric groups in more detail

Group	Standard generators	Conjugacy classes	Character information	Modular information	Permutation representations	Linear representations	Maximal subgroups
$\text{S}_\text{5}$	Yes	Yes	Complete	Complete	All primitive	All irreducibles in all characteristics	All, with SLPs with standard generators if applicable
$\text{S}_\text{6}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{S}_\text{7}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{S}_\text{8}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{S}_\text{9}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{S}_\text{10}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable
$\text{S}_\text{11}$	Yes	Yes	Complete	Complete	All primitive	All irreducible in positive characteristic	All, with SLPs with standard generators if applicable