Finite Group Databasebeta

← Prev (#46800228) Next (#46800230) →

C13×D1305 #46800229

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

Aliases

direct productC13×D1305
unambiguous semidirect productC5⋊(C13×D261)
unambiguous semidirect productC9⋊(C13×D145)
unambiguous semidirect productC29⋊(C13×D45)

Splittings

Fitting, HallC5×C9×C13×C29 ⋊ C2
derived, HallC5×C9×C29 ⋊ C2×C13
HallC9×C13×C29 ⋊ D5
HallC5×C13×C29 ⋊ D9
HallC5×C9×C13 ⋊ D29
HallC13×C29 ⋊ D45
HallC9×C29 ⋊ D5×C13
HallC5×C29 ⋊ C13×D9
HallC9×C13 ⋊ D145
HallC5×C13 ⋊ D261
HallC5×C9 ⋊ C13×D29
SylowC29 ⋊ C13×D45
SylowC9 ⋊ C13×D145
SylowC5 ⋊ C13×D261

Subgroups

subgroupG/H
center, hypercenterC13D1305
commutator, cosocle, hypocenterC5×C9×C29C2×C13
FrattiniC3C13×D435
FittingC5×C9×C13×C29C2
socleC3×C5×C13×C29D3
LCSG ▷ C5×C9×C29
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16965

Conjugacy classes & character table

8502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 15);