Finite Group Databasebeta

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C2×D3×#1393 #72270534

order1536
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×D3×#1393

Splittings

FittingC2×C3×#1393 ⋊ C2
SylowC3 ⋊ C22×#1393

Subgroups

subgroupG/H
centerC23D3×#99
commutatorC2×C3×C4C22×C42
FrattiniC22×D4C23×D3
FittingC2×C3×#1393C2
socleC23×C3C2×#99
prime radicalC23×D3×D4C22
cosocleC22×C3×D4C24
hypercenterC2×#1393D3
hypocenterC3C22×#1393
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C2×#1393

7604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 192

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#147779
maximal normal subgroup ofD3×#147779
maximal quotient ofC2×D3×#7307

GAP

Past the SmallGroups library coverage — no SmallGroups id.