Finite Group Databasebeta

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D3×#10620789 #72244198

order4032
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27

Aliases

direct productD3×#10620789

Splittings

FittingC24×C3×C7 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#120
SylowC7 ⋊ C3×D3×#120

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C3×C7C24×C3
FittingC24×C3×C7C22×C3
hypercenterC24D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×#120
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C24

2778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#120×AGL(1,𝔽7), C3⋊D3×#10620789, D3×#89804⋊C3
maximal normal subgroup ofD3×#120×AGL(1,𝔽7), D3×#89804⋊C3
maximal quotient ofD3×#90013⋊C3, D3×#13052144, C3⋊D3×#10620789

GAP

Past the SmallGroups library coverage — no SmallGroups id.