Finite Group Databasebeta

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C3×D3×#11717375 #72247697

order14400
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×D3×#11717375

Splittings

FittingC22×C32×C52 ⋊ C22×C4
HallC32×C52 ⋊ C2×C4×D4
SylowC52 ⋊ C3×C4×D3×D4
SylowC32 ⋊ C2×#11717375

Subgroups

subgroupG/H
centerC2×C3C2×D3×D5⋊AGL(1,𝔽5)
commutatorC2×C3×C52C23×C3×C4
FrattiniC2C2×C3×D3×D5⋊AGL(1,𝔽5)
FittingC22×C32×C52C22×C4
socleC2×C32×C52C23×C4
prime radicalC3×D3×#87886C2
cosocleC2×C3×C5⋊D5C24×C3
hypercenterC22×C3D3×D5⋊AGL(1,𝔽5)
hypocenterC3×C52C2×C3×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3 ◁ C22×C3

4594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,ℤ/9)×#11717375
maximal quotient ofAGL(1,ℤ/9)×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.