Finite Group Databasebeta

← Prev (#44544323) Next (#44544325) →

C3×#261×C41⋊C5 #44544324

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

Aliases

direct productC3×#261×C41⋊C5
unambiguous semidirect product(C3×C41×#261)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C4×C5
derived, HallC13×C41 ⋊ C3×C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC3×C41×#261 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC41×#261 ⋊ C3×C5
HallC3×C41 ⋊ C5×#261
SylowC41 ⋊ C3×C5×#261
HallC3×C13 ⋊ C4×C41⋊C5
SylowC13 ⋊ C3×C4×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#261×C41⋊C5
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC3×C13×C41C4×C5
prime radicalC3×D13×C41⋊C5C2
cosocleD13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 52);