Finite Group Databasebeta

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C5×C13×D261 #46800225

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

Aliases

direct productC5×C13×D261
unambiguous semidirect productC9⋊(C5×C13×D29)
unambiguous semidirect productC29⋊(C5×C13×D9)

Splittings

Fitting, HallC5×C9×C13×C29 ⋊ C2
derived, HallC9×C29 ⋊ C2×C5×C13
HallC9×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ D9
HallC5×C9×C29 ⋊ C2×C13
HallC5×C9×C13 ⋊ D29
HallC13×C29 ⋊ C5×D9
HallC5×C29 ⋊ C13×D9
HallC9×C13 ⋊ C5×D29
HallC5×C9 ⋊ C13×D29
SylowC29 ⋊ C5×C13×D9
SylowC9 ⋊ C5×C13×D29

Subgroups

subgroupG/H
center, hypercenterC5×C13D261
commutator, cosocle, hypocenterC9×C29C2×C5×C13
FrattiniC3C5×C13×D87
FittingC5×C9×C13×C29C2
socleC3×C5×C13×C29D3
LCSG ▷ C9×C29
UCSC1 ◁ C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 11);