Finite Group Databasebeta

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C3×C5×#126⋊C3 #13087789

order1440
isoclinismisoclinic class of #126⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×#126⋊C3
unambiguous semidirect product#126⋊(C32×C5)
unambiguous semidirect product(C3×#126)⋊(C3×C5)
unambiguous semidirect product(C5×#126)⋊C32
unambiguous semidirect product(C3×C5×#126)⋊C3

Splittings

FittingC3×C5×#126 ⋊ C3
derivedC42 ⋊ C2×C32×C5
HallC5×#126 ⋊ C32
Sylow#126 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5#126⋊C3
commutator, cosocle, hypocenterC42C2×C32×C5
FrattiniC22C2×C3×C5×A4
FittingC3×C5×#126C3
socleC22×C3×C5C2×A4
LCSG ▷ C42
UCSC1 ◁ C3×C5

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4106);