C₂×#11139 #357833

order	512
nilpotency class	3
isoclinism	isoclinic class of #2069
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

3114 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

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

maximal subgroup of	#72311305, C₂×#417702, C₂×#360531, …
maximal normal subgroup of	#72311305, C₂×#417702, C₂×#360531, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265029);