C₄²×D₃ #871

order	96
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = D₃×#87524 (order 2304) · Inn(G) = D₃ · Out(G) = #87524
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄²×D₃

Fitting	C₃×C₄² ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄²

108 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 78);