C₂×D₃×Q₈ #1005

order	96
automorphism	Aut(G) = D₃×#11713200 (order 4608) · Inn(G) = C₂²×D₃ · Out(G) = D₄×S₄
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×D₃×Q₈

Fitting	C₂×C₃×Q₈ ⋊ C₂
Sylow	C₃ ⋊ C₂²×Q₈

156 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 212);