C₂×#9019 #194711

order	512
nilpotency class	3
isoclinism	isoclinic class of #1595
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

3134 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	C₂×#208872, C₂×#208920, C₂×#194755, …
maximal normal subgroup of	C₂×#208872, C₂×#208920, C₂×#194755, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 101907);