C₃×Dic₃⋊C₈ #63600

order	288
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂⁶×D₃ (order 384) · Inn(G) = C₂×D₃ · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂×C₃×C₈ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×Dic₃⋊C₈
unambiguous semidirect product	Dic₃⋊(C₃×C₈)

C₃² ⋊ C₄⋊C₈

87 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 248);