Finite Group Databasebeta

← Prev (#44544274) Next (#44544276) →

C4×C5×C13⋊C3×C41 #44544275

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C13⋊C3×C41
unambiguous semidirect product(C4×C13)⋊(C3×C5×C41)
unambiguous semidirect product(C4×C5×C13)⋊(C3×C41)
unambiguous semidirect product(C4×C5×C13×C41)⋊C3

Splittings

Fitting, HallC4×C5×C13×C41 ⋊ C3
derived, SylowC13 ⋊ C3×C4×C5×C41
HallC5×C13×C41 ⋊ C3×C4
HallC4×C13×C41 ⋊ C3×C5
HallC13×C41 ⋊ C3×C4×C5
HallC4×C5×C13 ⋊ C3×C41
HallC5×C13 ⋊ C3×C4×C41
HallC4×C13 ⋊ C3×C5×C41

Subgroups

subgroupG/H
center, hypercenterC4×C5×C41C13⋊C3
commutator, hypocenterC13C3×C4×C5×C41
FrattiniC2C2×C5×C13⋊C3×C41
FittingC4×C5×C13×C41C3
socleC2×C5×C13×C41C2×C3
prime radicalC2×C5×C13⋊C3×C41C2
cosocleC2×C13C2×C3×C5×C41
LCSG ▷ C13
UCSC1 ◁ C4×C5×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10660

Conjugacy classes & character table

5740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 3);