Q₈×C₃⋊D₉ #88745

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

Aliases

Fitting	C₃×Q₈×C₉ ⋊ C₂
Sylow	C₃×C₉ ⋊ C₂×Q₈

190 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 392);