Finite Group Databasebeta

← Prev (#44544415) Next (#44544417) →

C3×D5×C13×D41 #44544416

order31980
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C13×D41
unambiguous semidirect product(D5×C41)⋊(C2×C3×C13)
unambiguous semidirect product(C5×D41)⋊(C2×C3×C13)
unambiguous semidirect productD205⋊(C2×C3×C13)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C22
derived, HallC5×C41 ⋊ C22×C3×C13
HallC5×C13×C41 ⋊ C22×C3
HallC3×C13×C41 ⋊ C2×D5
HallC3×C5×C41 ⋊ C22×C13
HallC13×C41 ⋊ C2×C3×D5
HallC3×C5×C13 ⋊ C2×D41
HallC3×C41 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C3×D41
SylowC41 ⋊ C2×C3×D5×C13
HallC3×C5 ⋊ C2×C13×D41
SylowC5 ⋊ C2×C3×C13×D41

Subgroups

subgroupG/H
center, hypercenterC3×C13D5×D41
commutator, cosocle, hypocenterC5×C41C22×C3×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C41C22
LCSG ▷ C5×C41
UCSC1 ◁ C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

3432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 144);