C₂×C₈×C₃⋊D₃ #64108

order	288
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂×C₈×C₃⋊D₃

Fitting	C₂×C₃²×C₈ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂²×C₈

228 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 756);