Finite Group Databasebeta

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C5×C7⋊(C9⋊#1181) #49141267

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

Aliases

direct productC5×C7⋊(C9⋊#1181)
unambiguous semidirect productC7⋊(C5×C9⋊#1181)
unambiguous semidirect productC9⋊(C5×C7⋊#1181)

Splittings

Fitting, HallC5×C7×C9×C29 ⋊ C4
derived, HallC7×C9×C29 ⋊ C4×C5
HallC5×C9×C29 ⋊ Dic7
HallC5×C7×C29 ⋊ Dic9
HallC5×C7×C9 ⋊ #1181
HallC9×C29 ⋊ C5×Dic7
HallC7×C29 ⋊ C5×Dic9
HallC5×C29 ⋊ Dic63
HallC7×C9 ⋊ C5×#1181
HallC5×C9 ⋊ C7⋊#1181
HallC5×C7 ⋊ C9⋊#1181
SylowC29 ⋊ C5×Dic63
SylowC9 ⋊ C5×C7⋊#1181
SylowC7 ⋊ C5×C9⋊#1181

Subgroups

subgroupG/H
center, hypercenterC5C7⋊(C9⋊#1181)
commutator, hypocenterC7×C9×C29C4×C5
FrattiniC3C5×C3⋊(C7⋊#1181)
FittingC5×C7×C9×C29C4
socleC3×C5×C7×C29Dic3
prime radicalC3×C5×C7×D29D3
cosocleC7×C9×D29C2×C5
LCSG ▷ C7×C9×C29
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

2535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 109);