C₂×#8921 #193177

order	512
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1818 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)(8,11)(9,13)(12,14)(15,16)(17,19)(18,21)(20,22);(3,5,6,4)(7,8,10,12)(9,14,13,11);(9,13)(11,14)(16,19)(17,22)(20,21)

maximal subgroup of	#72279313, #72279385, C₂×#210060
maximal normal subgroup of	#72279313, #72279385, C₂×#210060

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 100373);