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C5×C9⋊#10621728 #44477745

order30420
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9⋊#10621728
unambiguous semidirect productC9⋊(C5×#10621728)

Splittings

Fitting, HallC5×C9×C132 ⋊ C4
derived, HallC9×C132 ⋊ C4×C5
HallC5×C132 ⋊ Dic9
SylowC132 ⋊ C5×Dic9
HallC5×C9 ⋊ #10621728
SylowC9 ⋊ C5×#10621728

Subgroups

subgroupG/H
center, hypercenterC5C9⋊#10621728
commutator, hypocenterC9×C132C4×C5
FrattiniC3C5×C3⋊#10621728
FittingC5×C9×C132C4
socleC3×C5×C132Dic3
prime radicalC3×C5×C13⋊D13D3
cosocleC9×C13⋊D13C2×C5
LCSG ▷ C9×C132
UCSC1 ◁ C5

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 7605

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

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

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 334);