C₂×D₈×C₂₉ #11745334

order	928
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₈×C₂₉

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₂₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄×C₂₉ ◁ G

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4,5,6,7,8,9,10);(4,10)(5,9)(6,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(928, 193);