C₂×C₄²×Dic₃ #82051

order	384
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³ · Schur multiplier (H₂) = C₂³×C₄³

Aliases

direct product	C₂×C₄²×Dic₃
unambiguous semidirect product	(C₂×C₃)⋊C₄³

C₃ ⋊ C₂×C₄³

1272 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 384

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 14627);