C₉²×AGL(1,𝔽₅) #13108166

order	1620
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₉² · Schur multiplier (H₂) = C₉

Aliases

Fitting, Hall	C₅×C₉² ⋊ C₄
derived, Sylow	C₅ ⋊ C₄×C₉²

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 405

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5,6,7,8,9)(20,21,22,23);(10,11,12,13,14,15,16,17,18)(19,20,21,23,22)

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

maximal subgroup of	AGL(1,𝔽₅)×#6900, AGL(1,𝔽₅)×C₉⋊D₉, C₉×D₉×AGL(1,𝔽₅)
maximal normal subgroup of	AGL(1,𝔽₅)×#6900, AGL(1,𝔽₅)×C₉⋊D₉, C₉×D₉×AGL(1,𝔽₅)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 72);