C₂×#11880 #482054

order	512
nilpotency class	4
isoclinism	isoclinic class of #11753
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2506 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 18 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12,14,18,15,16,13,17);(4,8)(5,6)(9,10)(12,16);(3,5,7,6)(4,8,10,9)(11,13,15,14)(12,17,16,18)

maximal subgroup of	#72278528, C₂×#482377, #72278616, …
maximal normal subgroup of	#72278528, C₂×#482377, #72278616, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389250);