C₂×#12835 #493809

order	512
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1174 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 26 points:

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

maximal subgroup of	C₂×#495862, C₂×#497432, C₂×D₄×#367, …
maximal normal subgroup of	C₂×#495862, C₂×#497432, C₂×D₄×#367, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401005);