D₃×D₈ #910

order	96
automorphism	Aut(G) = C₂×D₃×AGL(1,ℤ/8) (order 384) · Inn(G) = D₃×D₄ · Out(G) = C₂³
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₃×D₈

Fitting	C₃×D₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₈

76 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 117);