Finite Group Databasebeta

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C5×C7×C9⋊#1181 #49141265

order36540
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C9⋊#1181
unambiguous semidirect productC9⋊(C5×C7×#1181)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C4
derived, HallC9×C29 ⋊ C4×C5×C7
HallC7×C9×C29 ⋊ C4×C5
HallC5×C9×C29 ⋊ C4×C7
HallC5×C7×C29 ⋊ Dic9
HallC5×C7×C9 ⋊ #1181
HallC7×C29 ⋊ C5×Dic9
HallC5×C29 ⋊ C7×Dic9
HallC7×C9 ⋊ C5×#1181
HallC5×C9 ⋊ C7×#1181
SylowC29 ⋊ C5×C7×Dic9
SylowC9 ⋊ C5×C7×#1181

Subgroups

subgroupG/H
center, hypercenterC5×C7C9⋊#1181
commutator, hypocenterC9×C29C4×C5×C7
FrattiniC3C5×C7×C3⋊#1181
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29Dic3
prime radicalC3×C5×C7×D29D3
cosocleC9×D29C2×C5×C7
LCSG ▷ C9×C29
UCSC1 ◁ C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

2625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 107);