C₂²×D₁₂ #1000

order	96
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = D₃×#72209832 (order 18432) · Inn(G) = C₂×D₃ · Out(G) = #72209653
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₁₂

Fitting	C₂²×C₃×C₄ ⋊ C₂
Sylow	C₃ ⋊ C₂²×D₄

236 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 207);