C₂×#62773 #10585951

order	512
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁷ · Schur multiplier (H₂) = C₂¹⁹

Aliases

	subgroup	G/H
center	C₂²×C₄	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁷
socle	C₂³	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂² ▷ C₁

38478 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 7 generators on 18 points:

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12)(13,17)(14,16)(15,18);(4,7)(8,10);(11,13)(12,15)(14,18)(16,17);(13,18)(15,17);(12,16)(15,17);(3,5,6,9)(4,8,7,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493147);