Finite Group Databasebeta

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C3×#11752022 #72230038

order2880
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#11752022

Splittings

HallC32×C5 ⋊ #386
SylowC32 ⋊ #65779
SylowC5 ⋊ C3×#5213

Subgroups

subgroupG/H
centerC22×C3C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×AGL(1,𝔽5)
FittingC23×C32×C5C2×C4
socleC22×C32×C5C22×C4
prime radicalC2×C3×D5×#67C2
cosocleC22×C3×D5C23×C3
hypercenterC23×C3D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C23×C3

1380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.