C₂×C₃×D₈ #972

order	96
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×#23882 (order 512) · Inn(G) = D₄ · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₃×D₈

	subgroup	G/H
center, socle	C₂²×C₃	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ G

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

(1,2)(3,4,5);(1,2)(7,10)(8,12)(11,13);(1,2)(6,7)(8,13)(9,11)(10,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 179);