C₂×#21441 #6372599

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

5512 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 18 points:

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

maximal subgroup of	C₂×#6573500, C₂×#6573502, C₂×M₁₆×#120
maximal normal subgroup of	C₂×#6573500, C₂×#6573502, C₂×M₁₆×#120

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279795);