C₇×C₄⋊Dic₃ #66614

order	336
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) = C₂×C₃×D₃×#120 (order 1152) · Inn(G) = C₂×D₃ · Out(G) = C₂²×C₃×D₄
homology	Abelianization (H₁) = C₂×C₄×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₄⋊Dic₃
unambiguous semidirect product	C₄⋊(C₇×Dic₃)

Hall	C₃×C₇ ⋊ C₄⋊C₄
Sylow	C₃ ⋊ C₇×C₄⋊C₄

52 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 336

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 83);