C₂×#11167 #357854

order	512
nilpotency class	3
isoclinism	isoclinic class of #8736
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

3106 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);(7,8,10,14,11,12,18,19)(9,15,17,22,16,13,20,21);(3,4)(5,6)(8,12)(10,18)(13,15)(17,20);(4,6)(7,9)(8,13,12,15)(10,17)(11,16)(14,21,19,22)(18,20)

maximal subgroup of	C₂×#417566, C₂×#374009, C₂×#133429
maximal normal subgroup of	C₂×#417566, C₂×#374009, C₂×#133429

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265050);