Finite Group Databasebeta

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C3×#11746527 #72260248

order2880
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#11746527

Splittings

HallC32×C5 ⋊ #339
SylowC32 ⋊ #64900
SylowC5 ⋊ C3×#4523

Subgroups

subgroupG/H
centerC3×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC3×C4×C5C3×C42
FrattiniC2×C4C3×D3×AGL(1,𝔽5)
FittingC2×C32×C4×C5C2×C4
socleC2×C32×C5#95
prime radicalC22×C32×D5D4
cosocleC2×C3×C4×D5C22×C3
hypercenterC2×C3×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#339
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72260257, C3×AGL(1,𝔽5)×#805, #72260286
maximal normal subgroup of#72260257, C3×AGL(1,𝔽5)×#805, #72260286

GAP

Past the SmallGroups library coverage — no SmallGroups id.