C₂×#8174 #182167

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

1998 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

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

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

maximal subgroup of	C₂×#210060, #72279471, #72279520, …
maximal normal subgroup of	C₂×#210060, #72279471, #72279520, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89363);