Finite Group Databasebeta

← Prev (#46800265) Next (#46800267) →

C3×C5×D1131 #46800266

order33930
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1131
unambiguous semidirect productC3⋊(C3×C5×D377)
unambiguous semidirect productC29⋊(C3×C5×D39)

Splittings

Fitting, socle, HallC32×C5×C13×C29 ⋊ C2
derivedC3×C13×C29 ⋊ C2×C3×C5
HallC32×C13×C29 ⋊ C2×C5
HallC5×C13×C29 ⋊ C3×D3
HallC32×C5×C29 ⋊ D13
HallC32×C5×C13 ⋊ D29
HallC13×C29 ⋊ C3×C5×D3
HallC32×C29 ⋊ C5×D13
HallC5×C29 ⋊ C3×D39
HallC32×C13 ⋊ C5×D29
HallC5×C13 ⋊ C3×D87
HallC32×C5 ⋊ D377
SylowC29 ⋊ C3×C5×D39
SylowC13 ⋊ C3×C5×D87
SylowC32 ⋊ C5×D377

Subgroups

subgroupG/H
center, hypercenterC3×C5D1131
commutator, cosocle, hypocenterC3×C13×C29C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C13×C29C2
LCSG ▷ C3×C13×C29
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11310

Conjugacy classes & character table

8505 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 52);