C₂×#33486 #7622673

order	512
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₆ · Schur multiplier (H₂) = C₂⁹

Aliases

1930 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4)(5,9)(6,8)(7,10)(11,12,13,16,14,17,19,22,15,18,20,23,21,24,25,26);(3,5)(4,7)(6,10)(8,9);(5,10)(7,9);(4,8)(7,9)

272 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₂×#7622691, C₂×#7624118, C₂×#7624119
maximal normal subgroup of	C₂×#7622691, C₂×#7624118, C₂×#7624119

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529869);