Finite Group Databasebeta

← Prev (#44544324) Next (#44544326) →

C3×#14523824⋊C5 #44544325

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

Aliases

direct productC3×#14523824⋊C5
unambiguous semidirect product(C3×#14523824)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C4×C5
derived, HallC13×C41 ⋊ C3×C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC3×#14523824 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
Hall#14523824 ⋊ C3×C5
HallC3×C41⋊C5 ⋊ Dic13
HallC41⋊C5 ⋊ C3×Dic13
HallC3×C41 ⋊ C5×Dic13
SylowC41 ⋊ C3×C5×Dic13
HallC3×C13 ⋊ #4223⋊C5
SylowC13 ⋊ C3×#4223⋊C5

Subgroups

subgroupG/H
center, hypercenterC3#14523824⋊C5
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC3×C13×C41C4×C5
prime radicalC3×C13×D41⋊C5C2
cosocleC13×D41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 53);