Finite Group Databasebeta

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C3×#13107590 #72231633

order4800
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#13107590

Splittings

FittingC23×C3×C52 ⋊ C2×C4
HallC3×C52 ⋊ #518
SylowC52 ⋊ C3×#518

Subgroups

subgroupG/H
centerC2×C3C22×D5⋊AGL(1,𝔽5)
commutatorC2×C52C23×C3×C4
FrattiniC2C22×C3×D5⋊AGL(1,𝔽5)
FittingC23×C3×C52C2×C4
socleC2×C3×C52C23×C4
prime radicalC2×C3×#87886C2
cosocleC2×C5⋊D5C24×C3
hypercenterC23×C3D5⋊AGL(1,𝔽5)
hypocenterC52C3×#518
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C3 ◁ C23×C3

1616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#72213412
maximal normal subgroup ofC3×#72213412

GAP

Past the SmallGroups library coverage — no SmallGroups id.