C₂²×#1848 #6371132

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

3226 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)(9,10,13,16,14,17,12,22)(11,18,20,23,21,24,19,15);(9,11,12,19,14,21,13,20)(10,15,16,18,17,23,22,24);(5,6,7,8)

maximal subgroup of	C₂²×#13185, C₂²×#22686, C₂²×#13213, …
maximal normal subgroup of	C₂²×#13185, C₂²×#22686, C₂²×#13213, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278328);