C₂×D₃×D₄ #1002

order	96
automorphism	Aut(G) = D₃×#23900 (order 1536) · Inn(G) = C₂²×D₃ · Out(G) = D₄²
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₃×D₄

Fitting	C₂×C₃×D₄ ⋊ C₂
Sylow	C₃ ⋊ C₂²×D₄

236 conjugacy classes of subgroups.

minimal degree	μ(G) = 9
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 4 generators on 9 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 209);