Finite Group Databasebeta

← Prev (#30630522) Next (#30630524) →

C3×D2665 #30630523

order15990
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D2665
unambiguous semidirect productC5⋊(C3×D533)
unambiguous semidirect productC41⋊(C3×D65)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C2
derived, HallC5×C13×C41 ⋊ C2×C3
HallC3×C13×C41 ⋊ D5
HallC3×C5×C41 ⋊ D13
HallC13×C41 ⋊ C3×D5
HallC5×C41 ⋊ C3×D13
HallC3×C5×C13 ⋊ D41
HallC3×C41 ⋊ D65
HallC5×C13 ⋊ C3×D41
SylowC41 ⋊ C3×D65
HallC3×C13 ⋊ D205
HallC3×C5 ⋊ D533
SylowC13 ⋊ C3×D205
SylowC5 ⋊ C3×D533

Subgroups

subgroupG/H
center, hypercenterC3D2665
commutator, cosocle, hypocenterC5×C13×C41C2×C3
FrattiniC1G
Fitting, socleC3×C5×C13×C41C2
LCSG ▷ C5×C13×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

4002 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×#24922519, C3×#24922520, C3×#24922523, …
maximal normal subgroup ofC3×#24922519, C3×#24922520, C3×#24922523, …
maximal quotient ofC3×Dic2665, C2×C3×D2665

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 11);