Finite Group Databasebeta

← Prev (#29503570) Next (#29503572) →

C5×C13×D13⋊C9 #29503571

order15210
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D13⋊C9
unambiguous semidirect productD13⋊(C5×C9×C13)
unambiguous semidirect product(C13⋊C9)⋊(C2×C5×C13)
unambiguous semidirect product(C5×D13)⋊(C9×C13)

Splittings

derivedC13 ⋊ C2×C5×C9×C13
HallC5×C13×C13⋊C9 ⋊ C2
HallC5×C13×D13 ⋊ C9
HallC13×C13⋊C9 ⋊ C2×C5
HallC5×C132 ⋊ C2×C9
HallC13×D13 ⋊ C5×C9
SylowC132 ⋊ C2×C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13D13⋊C3
commutator, hypocenterC13C2×C5×C9×C13
FrattiniC3C5×C13×D13⋊C3
Fitting, socleC3×C5×C132C2×C3
prime radicalC3×C5×C13×D13C3
cosocleC3×C13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C3×C5×C13

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1170

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13×#261⋊C9, C5×#20258778, C5×D13×D13⋊C9, …
maximal normal subgroup ofC5×C13×#261⋊C9, C5×#20258778, C5×D13×D13⋊C9, …
maximal quotient ofC5×C13×Dic13⋊C9, C2×C5×C13×D13⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15210, 34);