C₂×#8894 #192596

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

Aliases

1694 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)(7,8,10,13)(9,11,14,12)(15,16)(17,20)(18,21)(19,22);(3,5,6,4)(8,11)(9,14)(12,13)(16,20)(17,18)(21,22);(16,21)(17,18)(20,22)

maximal subgroup of	#72279300, #72279409, C₂×#210060
maximal normal subgroup of	#72279300, #72279409, C₂×#210060

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 99792);