C₂²×#2150 #7622515

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

2410 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2);(3,4);(6,8)(9,10,11,15,12,16,17,22,13,14,18,20,19,21,23,24);(5,6,7,8);(10,14)(15,20)(16,21)(22,24)

maximal subgroup of	C₂²×#13185, C₂²×#13255, C₂²×#12658, …
maximal normal subgroup of	C₂²×#13185, C₂²×#13255, C₂²×#12658, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529711);