Finite Group Databasebeta

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C3×#72224578 #72247627

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

Aliases

direct productC3×#72224578

Splittings

HallC32×C52 ⋊ C4×D4
SylowC52 ⋊ C3×C4×D12
SylowC32 ⋊ #11717375

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 radicalC3×#11925429C2
cosocleC2×C3×C5⋊D5C23×C3
hypocenterC3×C52C3×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3

1044 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, #72254716
maximal normal subgroup ofC3×D3×#11717375
maximal quotient of#72254716

GAP

Past the SmallGroups library coverage — no SmallGroups id.