Finite Group Databasebeta

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C3×D3×#87832 #72247679

order7200
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D3×#87832

Splittings

HallC32×C52 ⋊ C2×C4⋊C4
SylowC52 ⋊ C3×D3×C4⋊C4
SylowC32 ⋊ C2×#87832

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×D5⋊AGL(1,𝔽5)
commutatorC2×C3×C52C22×C3×C4
FrattiniC2C3×D3×D5⋊AGL(1,𝔽5)
Fitting, socleC2×C32×C52C22×C4
prime radicalC2×C3×D3×C5⋊D5C22
cosocleC2×C3×C5⋊D5C23×C3
hypocenterC3×C52C2×C3×C4⋊C4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3

1020 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×#11717375, AGL(1,ℤ/9)×#87832
maximal normal subgroup ofC3×D3×#11717375
maximal quotient ofAGL(1,ℤ/9)×#87832

GAP

Past the SmallGroups library coverage — no SmallGroups id.