C₃²×ΓL(1,𝔽₂₅) #88818

order	432
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

Fitting	C₃³×C₈ ⋊ C₂
Sylow	C₃³ ⋊ M₁₆

152 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 465);