Finite Group Databasebeta

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C2×D3×#1913 #72248185

order1536
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×D3×#1913

Splittings

FittingC2×C3×#1913 ⋊ C2
SylowC3 ⋊ C22×#1913

Subgroups

subgroupG/H
centerC22D3×#386
commutatorC23×C3C24×C4
FrattiniC24C24×D3
FittingC2×C3×#1913C2
socleC22×C3C2×#386
prime radicalC2×D3×#534C2
cosocleC24×C3C25
hypercenterC2×#1913D3
hypocenterC3C22×#1913
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C25 ◁ C2×#1913

15172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#394064, D3×#147819, C2×D3×#12753, …
maximal normal subgroup ofD3×#394064, D3×#147819, C2×D3×#12753, …
maximal quotient ofD3×#201664, C2×D3×#9495

GAP

Past the SmallGroups library coverage — no SmallGroups id.