C₂×C₇×Dic₆ #66715

order	336
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂×C₇×Dic₆
unambiguous semidirect product	(C₂×C₃)⋊(C₇×Q₈)

Hall	C₃×C₇ ⋊ C₂×Q₈
Sylow	C₃ ⋊ C₂×C₇×Q₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 336

A minimal faithful permutation representation — 3 generators on 20 points:

(3,4,5)(6,7,8,9,10,11,12)(13,15,16,20)(14,17,18,19);(1,2)(4,5)(13,14,16,18)(15,19,20,17);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(336, 184);