C₃²×D₃×Q₈ #89059

order	432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂²×C₃

Aliases

C₃²×D₃×Q₈

Fitting	C₃³×Q₈ ⋊ C₂
Sylow	C₃³ ⋊ C₂×Q₈

276 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 706);