Finite Group Databasebeta

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C3×D3×C22⋊#1044 #72247671

order7200
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C5

Aliases

direct productC3×D3×C22⋊#1044

Splittings

FittingC22×C32×C52 ⋊ C2×C4
HallC32×C52 ⋊ C2×C22⋊C4
SylowC52 ⋊ C3×D3×C22⋊C4
SylowC32 ⋊ C2×C22⋊#1044

Subgroups

subgroupG/H
centerC2×C3C2×D3×#1044
commutatorC2×C3×C52C22×C3×C4
FrattiniC2C2×C3×D3×#1044
FittingC22×C32×C52C2×C4
socleC2×C32×C52C22×C4
prime radicalC22×C3×D3×C5⋊D5C2
cosocleC2×C3×C5⋊D5C23×C3
hypercenterC22×C3D3×#1044
hypocenterC3×C52C2×C3×C22⋊C4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3 ◁ C22×C3

1692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×D3×#11717375, AGL(1,ℤ/9)×C22⋊#1044
maximal normal subgroup ofC3×D3×#11717375
maximal quotient ofAGL(1,ℤ/9)×C22⋊#1044

GAP

Past the SmallGroups library coverage — no SmallGroups id.