C₂×Q₈×C₃⋊D₃ #64362

order	288
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₂×Q₈×C₃⋊D₃

Fitting	C₂×C₃²×Q₈ ⋊ C₂
Sylow	C₃² ⋊ C₂²×Q₈

468 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 1010);