Finite Group Databasebeta

← Prev (#34062025) Next (#34062027) →

C13×D735 #34062026

order19110
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D735
unambiguous semidirect productC3⋊(C13×D245)
unambiguous semidirect productC5⋊(C13×D147)
unambiguous semidirect productC49⋊(C13×D15)

Splittings

Fitting, HallC3×C5×C13×C49 ⋊ C2
derived, HallC3×C5×C49 ⋊ C2×C13
HallC5×C13×C49 ⋊ D3
HallC3×C13×C49 ⋊ D5
HallC13×C49 ⋊ D15
HallC5×C49 ⋊ D3×C13
HallC3×C5×C13 ⋊ D49
HallC3×C49 ⋊ D5×C13
HallC5×C13 ⋊ D147
SylowC49 ⋊ C13×D15
HallC3×C13 ⋊ D245
HallC3×C5 ⋊ C13×D49
SylowC5 ⋊ C13×D147
SylowC3 ⋊ C13×D245

Subgroups

subgroupG/H
center, hypercenterC13D735
commutator, cosocle, hypocenterC3×C5×C49C2×C13
FrattiniC7C13×D105
FittingC3×C5×C13×C49C2
socleC3×C5×C7×C13D7
LCSG ▷ C3×C5×C49
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

4797 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD13×D735, C13×D15×D49, D637⋊D15, …
maximal normal subgroup ofD13×D735, C13×D15×D49, D637⋊D15, …
maximal quotient ofC13×Dic735, C2×C13×D735

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 19);