Finite Group Databasebeta

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C13×D1035 #41002088

order26910
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1035
unambiguous semidirect productC5⋊(C13×D207)
unambiguous semidirect productC9⋊(C13×D115)
unambiguous semidirect productC23⋊(C13×D45)

Splittings

Fitting, HallC5×C9×C13×C23 ⋊ C2
derived, HallC5×C9×C23 ⋊ C2×C13
HallC9×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ D9
HallC5×C9×C13 ⋊ D23
HallC13×C23 ⋊ D45
HallC9×C23 ⋊ D5×C13
HallC9×C13 ⋊ D115
HallC5×C23 ⋊ C13×D9
HallC5×C13 ⋊ D207
HallC5×C9 ⋊ C13×D23
SylowC23 ⋊ C13×D45
SylowC9 ⋊ C13×D115
SylowC5 ⋊ C13×D207

Subgroups

subgroupG/H
center, hypercenterC13D1035
commutator, cosocle, hypocenterC5×C9×C23C2×C13
FrattiniC3C13×D345
FittingC5×C9×C13×C23C2
socleC3×C5×C13×C23D3
LCSG ▷ C5×C9×C23
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6747 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 15);