Finite Group Databasebeta

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C2×D3×#2380 #72255146

order1536
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC2×D3×#2380

Splittings

FittingC2×C3×#2380 ⋊ C2
SylowC3 ⋊ C22×#2380

Subgroups

subgroupG/H
centerC24C24×D3
commutatorC22×C3C25×C4
FrattiniC23C25×D3
FittingC2×C3×#2380C2
socleC24×C3C25
prime radicalC22×D3×#127C2
cosocleC23×C3C26
hypercenterC2×#2380D3
hypocenterC3C22×#2380
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#2380

29604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#52004, D3×#512119, D3×#574938
maximal normal subgroup ofC2×D3×#52004, D3×#512119, D3×#574938

GAP

Past the SmallGroups library coverage — no SmallGroups id.