D₃×Q₈ #238

order	48
automorphism	Aut(G) = C₂×D₃×S₄ (order 288) · Inn(G) = C₂²×D₃ · Out(G) = C₂×D₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

D₃×Q₈

Fitting	C₃×Q₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(48, 40);