Finite Group Databasebeta

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C13×D1265 #45659773

order32890
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1265
unambiguous semidirect productC5⋊(C13×D253)
unambiguous semidirect productC11⋊(C13×D115)
unambiguous semidirect productC23⋊(C13×D55)

Splittings

Fitting, socle, HallC5×C11×C13×C23 ⋊ C2
derived, HallC5×C11×C23 ⋊ C2×C13
HallC11×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ D11
HallC5×C11×C13 ⋊ D23
HallC13×C23 ⋊ D55
HallC11×C23 ⋊ D5×C13
HallC11×C13 ⋊ D115
HallC5×C23 ⋊ C13×D11
HallC5×C13 ⋊ D253
HallC5×C11 ⋊ C13×D23
SylowC23 ⋊ C13×D55
SylowC11 ⋊ C13×D115
SylowC5 ⋊ C13×D253

Subgroups

subgroupG/H
center, hypercenterC13D1265
commutator, cosocle, hypocenterC5×C11×C23C2×C13
FrattiniC1G
Fitting, socleC5×C11×C13×C23C2
LCSG ▷ C5×C11×C23
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16445

Conjugacy classes & character table

8242 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32890, 16);