C₄×D₃×C₈ #4684

order	192
isoclinism	isoclinic class of D₃
automorphism	Aut(G) = D₃×#394058 (order 3072) · Inn(G) = D₃ · Out(G) = #394058
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₄×D₃×C₈

Fitting	C₃×C₄×C₈ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₄×C₈

162 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 15 points:

(2,3);(1,2,3)(8,9,10,12,11,13,14,15);(4,5,6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 243);