C₂×#33418 #7622545

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

2006 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)(5,8)(6,7)(9,10)(11,12,13,17,14,18,19,24,15,16,20,22,21,23,25,26);(4,7)(8,10);(3,5,6,9)(4,8,7,10);(12,16)(17,22)(18,23)(24,26)

maximal subgroup of	C₂×#126586, C₂×#493177, #72213483, …
maximal normal subgroup of	C₂×#126586, C₂×#493177, #72213483, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529741);