C₉×#16810003 #44477730

order	30420
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×#16810003

Splittings

Fitting, Hall	C₅×C₉×C₁₃² ⋊ C₄
derived, Hall	C₅×C₁₃² ⋊ C₄×C₉
Hall	C₉×C₁₃² ⋊ AGL(1,𝔽₅)
Sylow	C₁₃² ⋊ C₉×AGL(1,𝔽₅)
Hall	C₅×C₉ ⋊ #10621728
Sylow	C₅ ⋊ C₉×#10621728

Subgroups

	subgroup	G/H
center, hypercenter	C₉	#16810003
commutator, hypocenter	C₅×C₁₃²	C₄×C₉
Frattini	C₃	C₃×#16810003
Fitting	C₅×C₉×C₁₃²	C₄
socle	C₃×C₅×C₁₃²	C₃×C₄
prime radical, cosocle	C₃×C₅⋊(C₁₃⋊D₁₃)	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₉

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 7605

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5,6,7,8,9)(11,12,13,14)(16,17,18,20)(19,22,23,27)(21,25,26,24)(29,30,31,33)(32,35,36,40)(34,38,39,37);(10,11,12,14,13)(28,29,32,35,39,33,37,38,30,34,40,36,31);(15,16,19,22,26,20,24,25,17,21,27,23,18)

Conjugacy classes & character table

1935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 319);

C9×#16810003 #44477730