Finite Group Databasebeta

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C3×C5×D361⋊C3 #44570434

order32490
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×D361⋊C3
unambiguous semidirect productD361⋊(C32×C5)
unambiguous semidirect product(C361⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C3×D361)⋊(C3×C5)
unambiguous semidirect product(C5×D361)⋊C32
unambiguous semidirect product(C3×C5×D361)⋊C3

Splittings

FittingC3×C5×C361 ⋊ C2×C3
derived, SylowC361 ⋊ C2×C32×C5
HallC3×C5×C361⋊C3 ⋊ C2
HallC5×D361 ⋊ C32
HallC3×C361⋊C3 ⋊ C2×C5
HallC5×C361 ⋊ C2×C32
HallD361 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5D361⋊C3
commutator, cosocle, hypocenterC361C2×C32×C5
FrattiniC19C3×C5×D19⋊C3
FittingC3×C5×C361C2×C3
socleC3×C5×C19D19⋊C3
LCSG ▷ C361
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5415

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 18);