Finite Group Databasebeta

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D3×C3⋊D3×#102 #72268957

order3456
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C3

Aliases

direct productD3×C3⋊D3×#102

Splittings

FittingC33×#102 ⋊ C22
SylowC33 ⋊ C22×#102

Subgroups

subgroupG/H
centerC22D3×D4×C3⋊D3
commutatorC33×C4C23×C4
FrattiniC2×C4C22×D3×C3⋊D3
FittingC33×#102C22
socleC22×C33C22×D4
prime radicalC2×D3×D4×C3⋊D3C2
cosocleC2×C33×C4C24
hypercenter#102D3×C3⋊D3
hypocenterC33C22×#102
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

7240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C3⋊D3×#442
maximal normal subgroup ofD3×C3⋊D3×#442

GAP

Past the SmallGroups library coverage — no SmallGroups id.