Finite Group Databasebeta

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C2×C5×D3×C9 #10587406

order540
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D3×C9
unambiguous semidirect productC3⋊(C22×C5×C9)
unambiguous semidirect product(C2×C3)⋊(C2×C5×C9)

Splittings

FittingC2×C3×C5×C9 ⋊ C2
derivedC3 ⋊ C22×C5×C9
HallC3×C5×C9 ⋊ C22
SylowC3×C9 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D3
commutator, hypocenterC3C22×C5×C9
FrattiniC3C2×C3×C5×D3
FittingC2×C3×C5×C9C2
socleC2×C32×C5C2×C3
prime radicalC2×C3×C5×D3C3
cosocleC32C22×C3×C5
LCSG ▷ C3
UCSC1 ◁ C2×C5×C9

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD3×C9×Dic5, C9×#1201, C9×#1203, …
maximal normal subgroup ofD3×C9×Dic5, C9×#1201, C9×#1203, …
maximal quotient ofC5×C9×Dic6, C4×C5×D3×C9, C5×C9×D12, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 66);