#41×M₃₂ #7622668

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁸

Aliases

1535 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	M₃₂×#131, #72287744, #72287757, …
maximal normal subgroup of	M₃₂×#131, #72287744, #72287757, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529864);