C₃×C₄×C₃⋊Dic₃ #88840

order	432
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₃×C₄

Aliases

derived	C₃² ⋊ C₃×C₄²
Sylow	C₃³ ⋊ C₄²

244 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 487);