C₃×C₄⋊Dic₇ #66598

order	336
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₄⋊Dic₇
unambiguous semidirect product	C₄⋊(C₃×Dic₇)

Hall	C₃×C₇ ⋊ C₄⋊C₄
Sylow	C₇ ⋊ C₃×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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 67);