Finite Group Databasebeta

← Prev (#34062143) Next (#34062145) →

C13×C5⋊#64422 #34062144

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊#64422
unambiguous semidirect productC5⋊(C13×#64422)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C13
HallC5×C13×#3862 ⋊ C2
HallC7×C13×D35 ⋊ C3
HallC13×#3862 ⋊ D5
HallC5×#3862 ⋊ C2×C13
HallC72×C13 ⋊ C3×D5
HallC7×D35 ⋊ C3×C13
Hall#3862 ⋊ D5×C13
HallC5×C13 ⋊ #64422
SylowC72 ⋊ C3×D5×C13
SylowC5 ⋊ C13×#64422

Subgroups

subgroupG/H
center, hypercenterC13C5⋊#64422
commutator, cosocle, hypocenterC5×C72C2×C3×C13
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C13

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD13×C5⋊#64422, D5×C13×#64422, #50304175, …
maximal normal subgroup ofD13×C5⋊#64422, D5×C13×#64422, #50304175, …
maximal quotient ofC13×#15668737, C2×C13×C5⋊#64422

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 137);