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C22×C5×(C3⋊D3)⋊C3 #11762004

order1080
isoclinismisoclinic class of (C3⋊D3)⋊C3
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23×C3

Aliases

direct productC22×C5×(C3⋊D3)⋊C3

Splittings

FittingC22×C5×H(3,𝔽3) ⋊ C2
derivedC32 ⋊ C23×C3×C5
HallC5×H(3,𝔽3) ⋊ C23
SylowH(3,𝔽3) ⋊ C23×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5(C3⋊D3)⋊C3
commutator, cosocle, hypocenterC32C23×C3×C5
FrattiniC3C22×C3×C5×D3
FittingC22×C5×H(3,𝔽3)C2
socleC22×C3×C5C3×D3
LCSG ▷ C32
UCSC1 ◁ C22×C5

244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 180

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C5×PSU(3,𝔽2)⋊C3, C22×C3×C5×(C3⋊D3)⋊C3, C22×C5×((C3⋊D3)⋊C3)⋊C2, …
maximal normal subgroup ofC22×C3×C5×(C3⋊D3)⋊C3, C22×C5×((C3⋊D3)⋊C3)⋊C2, C2×C4×C5×(C3⋊D3)⋊C3
maximal quotient ofC22×C3×C5×(C3⋊D3)⋊C3, C2×C4×C5×(C3⋊D3)⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 350);