C₂×C₈×C₃⋊C₈ #69720

order	384
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₈² · Schur multiplier (H₂) = C₂²×C₈

Aliases

direct product	C₂×C₈×C₃⋊C₈
unambiguous semidirect product	(C₂×C₃)⋊C₈²

C₃ ⋊ C₂×C₈²

280 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 384

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(4,5)(6,7,8,10,9,11,12,13);(3,4,5)(14,15,16,18,17,19,20,21);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 2296);