Finite Group Databasebeta

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C2×C3×#92283 #72254024

order2916
automorphism?
homologyAbelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33

Aliases

direct productC2×C3×#92283

Splittings

FittingC2×C3×#6910 ⋊ C2
SylowC3×#6910 ⋊ C22

Subgroups

subgroupG/H
center, socleC2×C32C3×(C3⋊D3)⋊C3
commutator, cosocle, hypocenterH(3,𝔽3)C22×C33
FrattiniC32C2×C33×D3
FittingC2×C3×#6910C2
prime radicalC2×C32×#272C3
hypercenterC2×C33(C3⋊D3)⋊C3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C32 ◁ C2×C33

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 162

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal quotient ofC2×#72221896

GAP

Past the SmallGroups library coverage — no SmallGroups id.