C₂×#8818 #191423

order	512
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₈

Aliases

1202 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4,5,6)(8,11)(9,12)(13,14)(16,19)(17,20)(21,22);(7,8,12,14,10,13,9,11);(15,16,20,22,18,21,17,19)

maximal subgroup of	#72242467, C₂×C₄×#1712
maximal normal subgroup of	#72242467, C₂×C₄×#1712

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 98619);