Finite Group Databasebeta

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C5×C9×C13⋊C3 #13182170

order1755
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C9 · Schur multiplier (H2) = C3

Aliases

direct productC5×C9×C13⋊C3

Splittings

FittingC5×C9×C13 ⋊ C3
derived, SylowC13 ⋊ C3×C5×C9
HallC5×C13 ⋊ C3×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9C13⋊C3
commutator, hypocenterC13C3×C5×C9
FrattiniC3C3×C5×C13⋊C3
FittingC5×C9×C13C3
socleC3×C5×C13C32
prime radicalC3×C5×C13⋊C3C3
cosocleC3×C13C32×C5
LCSG ▷ C13
UCSC1 ◁ C5×C9

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 585

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1755, 3);