C₃×C₅×Dic₆ #67165

order	360
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₄×D₃×D₄ (order 384) · Inn(G) = C₂×D₃ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₅×Dic₆
unambiguous semidirect product	C₃⋊(C₃×C₅×Q₈)

Hall	C₃²×C₅ ⋊ Q₈
Sylow	C₃² ⋊ C₅×Q₈

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,3)(4,5,6)(7,14,10,9)(8,13,12,11)(15,16,17,18,19);(5,6)(7,12,10,8)(9,11,14,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(360, 95);