C₃×D₈ #223

order	48
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×AGL(1,ℤ/8) (order 64) · Inn(G) = D₄ · Out(G) = C₂³
holomorph	G ⋊ Aut(G) = D₃×#489347
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₈

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

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 25);