Finite Group Databasebeta

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C3×#10948663 #72222786

order2304
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC3×#10948663

Splittings

SylowC32 ⋊ #33471

Subgroups

subgroupG/H
centerC2×C3C2×#5152
commutatorC3×C8C23×C3×C4
FrattiniC2×C8C23×C3×D3
Fitting, prime radicalC2×C32×#509C2
socleC2×C32C2×#442
cosocleC2×C3×C8C24×C3
hypercenterC2×C3×#509D3
hypocenterC3C3×#33471
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#509

1536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#72228227
maximal normal subgroup ofC3×#72228227

GAP

Past the SmallGroups library coverage — no SmallGroups id.