C₂×#12004 #483329

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

638 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);(4,7)(5,8)(9,10)(11,12,13,17,14,18,19,24,15,16,20,22,21,23,25,26);(3,4,8,10,6,9,5,7);(12,16)(17,22)(18,23)(24,26)

maximal subgroup of	C₂×#135732, #72210437
maximal normal subgroup of	C₂×#135732, #72210437

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390525);