Finite Group Databasebeta

← Prev (#44544275) Next (#44544277) →

C4×C13⋊C3×C41⋊C5 #44544276

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

Aliases

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

Splittings

Fitting, HallC4×C13×C41 ⋊ C3×C5
derived, HallC13×C41 ⋊ C3×C4×C5
HallC4×C13×C41⋊C5 ⋊ C3
HallC4×C13⋊C3×C41 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC13⋊C3×C41 ⋊ C4×C5
HallC4×C41 ⋊ C5×C13⋊C3
HallC4×C13 ⋊ C3×C41⋊C5
SylowC41 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C4×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC4C13⋊C3×C41⋊C5
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC2C2×C13⋊C3×C41⋊C5
FittingC4×C13×C41C3×C5
socle, cosocleC2×C13×C41C2×C3×C5
prime radicalC2×C13⋊C3×C41⋊C5C2
LCSG ▷ C13×C41
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2132

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 4);