Finite Group Databasebeta

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C2×D3×#2846 #72246175

order1536
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C218

Aliases

direct productC2×D3×#2846

Splittings

FittingC2×C3×#2846 ⋊ C2
SylowC3 ⋊ C22×#2846

Subgroups

subgroupG/H
centerC24C24×D3
commutator, cosocleC23×C3C26
FrattiniC23C25×D3
FittingC2×C3×#2846C2
socleC24×C3C25
hypercenterC2×#2846D3
hypocenterC3C22×#2846
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#2846

447100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×#394058, D3×#115690, D3×#846041, …
maximal normal subgroup ofD3×#394058, D3×#115690, D3×#846041, …
maximal quotient ofD3×#612424, C2×D3×#32898, D3×#6628842, …
automorphism group of#4689, #4708

GAP

Past the SmallGroups library coverage — no SmallGroups id.