C₂×#11200 #357899

order	512
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

3858 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);(8,9)(11,12,13,14)(15,16)(17,19)(18,20)(21,22);(3,4)(5,6)(7,8)(9,10)(16,19)(20,21);(4,6)(7,9,10,8)(16,20)(18,22)(19,21)

maximal subgroup of	#72314134, #72314156, #72314163
maximal normal subgroup of	#72314134, #72314156, #72314163

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265095);