Finite Group Databasebeta

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C13×C3⋊(#4223⋊C5) #44544327

order31980
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(#4223⋊C5)
unambiguous semidirect productC3⋊(C13×#4223⋊C5)
unambiguous semidirect product(C3⋊#4223)⋊(C5×C13)
unambiguous semidirect product(C13×C3⋊#4223)⋊C5

Splittings

Fitting, socle, HallC3×C13×C41 ⋊ C4×C5
derived, HallC3×C41 ⋊ C4×C5×C13
HallC3×C13×C41⋊C5 ⋊ C4
HallC13×C3⋊#4223 ⋊ C5
HallC13×C41⋊C5 ⋊ Dic3
HallC3×C41⋊C5 ⋊ C4×C13
HallC13×C41 ⋊ C5×Dic3
HallC3⋊#4223 ⋊ C5×C13
HallC41⋊C5 ⋊ Dic3×C13
SylowC41 ⋊ C5×Dic3×C13
HallC3×C13 ⋊ #4223⋊C5
SylowC3 ⋊ C13×#4223⋊C5

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(#4223⋊C5)
commutator, hypocenterC3×C41C4×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C41C4×C5
prime radicalC3×C13×D41⋊C5C2
cosocleC3×D41C2×C5×C13
LCSG ▷ C3×C41
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 55);