Finite Group Databasebeta

← Prev (#44526517) Next (#44526519) →

C3×C5×C13⋊C3×C53 #44526518

order31005
automorphism?
homologyAbelianization (H1) = C32×C5×C53 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C13⋊C3×C53
unambiguous semidirect productC13⋊(C32×C5×C53)
unambiguous semidirect product(C3×C13)⋊(C3×C5×C53)
unambiguous semidirect product(C5×C13)⋊(C32×C53)
unambiguous semidirect product(C3×C5×C13)⋊(C3×C53)
unambiguous semidirect product(C13×C53)⋊(C32×C5)
unambiguous semidirect product(C3×C13×C53)⋊(C3×C5)
unambiguous semidirect product(C5×C13×C53)⋊C32
unambiguous semidirect product(C3×C5×C13×C53)⋊C3

Splittings

Fitting, socleC3×C5×C13×C53 ⋊ C3
derived, SylowC13 ⋊ C32×C5×C53
HallC5×C13×C53 ⋊ C32
HallC13×C53 ⋊ C32×C5
HallC5×C13 ⋊ C32×C53

Subgroups

subgroupG/H
center, hypercenterC3×C5×C53C13⋊C3
commutator, cosocle, hypocenterC13C32×C5×C53
FrattiniC1G
Fitting, socleC3×C5×C13×C53C3
LCSG ▷ C13
UCSC1 ◁ C3×C5×C53

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10335

Conjugacy classes & character table

5565 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31005, 6);