Finite Group Databasebeta

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C3×C5×C13×D87 #46800264

order33930
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×D87
unambiguous semidirect productC3⋊(C3×C5×C13×D29)
unambiguous semidirect productC29⋊(C3×C5×D3×C13)

Splittings

Fitting, socle, HallC32×C5×C13×C29 ⋊ C2
derivedC3×C29 ⋊ C2×C3×C5×C13
HallC32×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ C3×D3
HallC32×C5×C29 ⋊ C2×C13
HallC32×C5×C13 ⋊ D29
HallC13×C29 ⋊ C3×C5×D3
HallC32×C29 ⋊ C2×C5×C13
HallC5×C29 ⋊ C3×D3×C13
HallC32×C13 ⋊ C5×D29
HallC32×C5 ⋊ C13×D29
SylowC29 ⋊ C3×C5×D3×C13
SylowC32 ⋊ C5×C13×D29

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13D87
commutator, cosocle, hypocenterC3×C29C2×C3×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C13×C29C2
LCSG ▷ C3×C29
UCSC1 ◁ C3×C5×C13

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11310

Conjugacy classes & character table

8775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 50);