Finite Group Databasebeta

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C2×D3×#1783 #72248057

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productC2×D3×#1783

Splittings

FittingC2×C3×#1783 ⋊ C2
SylowC3 ⋊ C22×#1783

Subgroups

subgroupG/H
centerC23C2×D3×C22⋊C4
commutatorC23×C3C24×C4
FrattiniC22×C4C24×D3
FittingC2×C3×#1783C2
socleC23×C3C22×C22⋊C4
prime radicalC24×D3×D4C2
cosocleC22×C3×C4C25
hypercenterC2×#1783D3
hypocenterC3C22×#1783
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#1783

59732 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#147555, C2×D3×#30434, D3×#147567, …
maximal normal subgroup ofD3×#147555, C2×D3×#30434, D3×#147567, …
maximal quotient ofD3×#392113

GAP

Past the SmallGroups library coverage — no SmallGroups id.