Finite Group Databasebeta

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C3×D5⋊#806 #72230054

order2880
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC3×D5⋊#806

Splittings

HallC32×C5 ⋊ C2×#99
SylowC32 ⋊ D5⋊#99
SylowC5 ⋊ C2×C3×#806

Subgroups

subgroupG/H
centerC2×C3C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC22×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×AGL(1,𝔽5)
FittingC23×C32×C5C2×C4
socleC2×C32×C5C2×C22⋊C4
prime radicalC2×C3×D5×#67C2
cosocleC22×C3×D5C23×C3
hypercenterC23×C3D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C3×#99
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C23×C3

972 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.