C₃²×C₉×AGL(1,𝔽₅) #13108359

order	1620
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₉ · Schur multiplier (H₂) = C₃³

Aliases

Fitting, Hall	C₃²×C₅×C₉ ⋊ C₄
derived, Sylow	C₅ ⋊ C₃²×C₄×C₉

300 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 405

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

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

405 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 265);