Finite Group Databasebeta

← Prev (#30630526) Next (#30630528) →

C5×D1599 #30630527

order15990
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1599
unambiguous semidirect productC3⋊(C5×D533)
unambiguous semidirect productC13⋊(C5×D123)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C2
derived, HallC3×C13×C41 ⋊ C2×C5
HallC5×C13×C41 ⋊ D3
HallC3×C5×C41 ⋊ D13
HallC13×C41 ⋊ C5×D3
HallC5×C41 ⋊ D39
HallC3×C5×C13 ⋊ D41
HallC3×C41 ⋊ C5×D13
HallC5×C13 ⋊ D123
SylowC41 ⋊ C5×D39
HallC3×C13 ⋊ C5×D41
HallC3×C5 ⋊ D533
SylowC13 ⋊ C5×D123
SylowC3 ⋊ C5×D533

Subgroups

subgroupG/H
center, hypercenterC5D1599
commutator, cosocle, hypocenterC3×C13×C41C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C41C2
LCSG ▷ C3×C13×C41
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

4005 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D39×D41, C5×D13×D123, C5×D3×D533, …
maximal normal subgroup ofC5×D39×D41, C5×D13×D123, C5×D3×D533, …
maximal quotient ofC5×Dic1599, C2×C5×D1599

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 15);