C₂×#11440 #480021

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

1270 conjugacy classes of subgroups.

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

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

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

maximal subgroup of	C₂×#480075, C₂×#128382, C₂×#128384
maximal normal subgroup of	C₂×#480075, C₂×#128382, C₂×#128384

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387217);