Finite Group Databasebeta

← Prev (#44544468) Next (#44544470) →

D3×C13×D205 #44544469

order31980
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×C13×D205
unambiguous semidirect product(C5×D3)⋊(C13×D41)
unambiguous semidirect product(D3×C41)⋊(D5×C13)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C22
derived, HallC3×C5×C41 ⋊ C22×C13
HallC5×C13×C41 ⋊ C2×D3
HallC3×C13×C41 ⋊ C2×D5
HallC13×C41 ⋊ D3×D5
HallC5×C41 ⋊ C2×D3×C13
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×D5×C13
HallC5×C13 ⋊ D3×D41
SylowC41 ⋊ D3×D5×C13
HallC3×C13 ⋊ C2×D205
HallC3×C5 ⋊ C2×C13×D41
SylowC5 ⋊ D3×C13×D41
SylowC3 ⋊ C2×C13×D205

Subgroups

subgroupG/H
center, hypercenterC13D3×D205
commutator, cosocle, hypocenterC3×C5×C41C22×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C41C22
LCSG ▷ C3×C5×C41
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

4056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 197);