Finite Group Databasebeta

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C3×#72224574 #72247648

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

Aliases

direct productC3×#72224574

Splittings

FittingC22×C32×C52 ⋊ C2×C4
HallC32×C52 ⋊ C4×D4
SylowC52 ⋊ C3×D4×Dic3
SylowC32 ⋊ #11717375

Subgroups

subgroupG/H
centerC2×C3C2×D5⋊ΓL(1,𝔽16)
commutatorC2×C3×C52C22×C3×C4
FrattiniC2C2×C3×D5⋊ΓL(1,𝔽16)
FittingC22×C32×C52C2×C4
socleC2×C32×C52C22×C4
prime radicalC32×#87886C2
cosocleC2×C3×C5⋊D5C23×C3
hypercenterC22×C3D5⋊ΓL(1,𝔽16)
hypocenterC3×C52C3×C4×D4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2×C3 ◁ C22×C3

1108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D3×#11717375, #72254787
maximal normal subgroup ofC3×D3×#11717375
maximal quotient of#72254787

GAP

Past the SmallGroups library coverage — no SmallGroups id.