AGL(1,𝔽₅)×C₃²⋊C₉ #13108167

order	1620
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₉ · Schur multiplier (H₂) = C₃²

Aliases

direct product	AGL(1,𝔽₅)×C₃²⋊C₉
unambiguous semidirect product	(C₃²×AGL(1,𝔽₅))⋊C₉

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

138 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 135

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

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

maximal subgroup of	AGL(1,𝔽₅)×#6891, AGL(1,𝔽₅)×#4181, AGL(1,𝔽₅)×(C₃⋊D₃)⋊C₉, …
maximal normal subgroup of	AGL(1,𝔽₅)×#6891, AGL(1,𝔽₅)×#4181, AGL(1,𝔽₅)×(C₃⋊D₃)⋊C₉, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 73);