Finite Group Databasebeta

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C2×D3×C9×D5 #11761982

order1080
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C23

Aliases

direct productC2×D3×C9×D5
unambiguous semidirect product(C5×D3)⋊(C22×C9)
unambiguous semidirect product(C3×D5)⋊(C22×C9)
unambiguous semidirect productD15⋊(C22×C9)

Splittings

FittingC2×C3×C5×C9 ⋊ C22
derivedC3×C5 ⋊ C23×C9
HallC3×C5×C9 ⋊ C23
SylowC3×C9 ⋊ C22×D5
SylowC5 ⋊ C22×D3×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9D3×D5
commutator, hypocenterC3×C5C23×C9
FrattiniC3C2×C3×D3×D5
FittingC2×C3×C5×C9C22
socleC2×C32×C5C22×C3
prime radicalC2×C3×D3×D5C3
cosocleC32×C5C23×C3
LCSG ▷ C3×C5
UCSC1 ◁ C2×C9

212 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 328);