Finite Group Databasebeta

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D3×#20959 #72248798

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

Aliases

direct productD3×#20959

Splittings

FittingC3×#20959 ⋊ C2
SylowC3 ⋊ C2×#20959

Subgroups

subgroupG/H
centerC2×C4D3×#120
commutatorC23×C3C24×C4
FrattiniC24C24×D3
FittingC3×#20959C2
socleC22×C3C22×#120
prime radicalC2×D3×#525C2
cosocleC24×C3C25
hypercenter#20959D3
hypocenterC3C2×#20959
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #20959

14236 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×#417670, D3×#364592, D3×#6437616, …
maximal normal subgroup ofD3×#417670, D3×#364592, D3×#6437616, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.