Finite Group Databasebeta

← Prev (#44570440) Next (#44570442) →

C2×C3×C5×C361⋊C3 #44570441

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

Aliases

direct productC2×C3×C5×C361⋊C3
unambiguous semidirect product(C2×C361)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C361)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C361)⋊C32
unambiguous semidirect product(C2×C3×C5×C361)⋊C3

Splittings

FittingC2×C3×C5×C361 ⋊ C3
derived, SylowC361 ⋊ C2×C32×C5
HallC2×C5×C361 ⋊ C32
HallC5×C361 ⋊ C2×C32
HallC2×C361 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C361⋊C3
commutator, cosocle, hypocenterC361C2×C32×C5
FrattiniC19C2×C3×C5×C19⋊C3
FittingC2×C3×C5×C361C3
socleC2×C3×C5×C19C19⋊C3
LCSG ▷ C361
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10830

Conjugacy classes & character table

3690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 25);