Finite Group Databasebeta

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C3×#11756846 #72230061

order2880
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#11756846

Splittings

FittingC32×C5×D4 ⋊ C2×C4
HallC32×C5 ⋊ #520
SylowC32 ⋊ #66266
SylowC5 ⋊ C3×#5546

Subgroups

subgroupG/H
centerC2×C3C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C23×C3×C4
FrattiniC2C22×C3×D3×AGL(1,𝔽5)
FittingC32×C5×D4C2×C4
socleC2×C32×C5C23×C4
prime radicalC3×D5×#237C2
cosocleC2×C3×D5C24×C3
hypercenterC3×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C3×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×D4

1270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72260225, C3×AGL(1,𝔽5)×#1004, #72260263
maximal normal subgroup of#72260225, C3×AGL(1,𝔽5)×#1004, #72260263

GAP

Past the SmallGroups library coverage — no SmallGroups id.