Finite Group Databasebeta

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D3×#11101 #72253285

order1536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productD3×#11101

Splittings

FittingC3×#11101 ⋊ C2
SylowC3 ⋊ C2×#11101

Subgroups

subgroupG/H
centerC2×C4D3×#127
commutatorC22×C3×C4C23×C4
FrattiniC23×C4C23×D3
FittingC3×#11101C2
socleC22×C3C2×#399
prime radicalC25×D3Q8
cosocleC23×C3×C4C24
hypercenter#11101D3
hypocenterC3C2×#11101
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #11101

6348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#417674, D3×#454002, D3×#418876, …
maximal normal subgroup ofD3×#417674, D3×#454002, D3×#418876, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.