Finite Group Databasebeta

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C3⋊#261×C41⋊C5 #44544332

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

Aliases

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

Splittings

Fitting, socle, derived, HallC3×C13×C41 ⋊ C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC41×C3⋊#261 ⋊ C5
HallC13×C41⋊C5 ⋊ Dic3
HallC3×C41⋊C5 ⋊ #261
HallC13×C41 ⋊ C5×Dic3
HallC3×C41 ⋊ C5×#261
SylowC41 ⋊ C5×C3⋊#261
HallC3×C13 ⋊ C4×C41⋊C5
SylowC13 ⋊ Dic3×C41⋊C5
SylowC3 ⋊ #261×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C13×C41C4×C5
prime radicalC3×D13×C41⋊C5C2
cosocleC3×D13×C41C2×C5
LCSG ▷ C3×C13×C41
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1599

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 60);