C₂×#11300 #358330

order	512
nilpotency class	3
isoclinism	isoclinic class of #8603
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1610 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);(7,8,11,15,12,16,10,13)(9,17,18,14,20,21,19,22);(3,4)(5,6)(8,13,16,15)(14,21,22,17);(4,6)(7,9,10,18,12,20,11,19)(8,14,15,17,16,22,13,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265526);