Finite Group Databasebeta

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D3×ΓL(1,𝔽8)×#99 #72254377

order4032
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productD3×ΓL(1,𝔽8)×#99

Splittings

FittingC3×C7×#99 ⋊ C2×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#99
SylowC7 ⋊ C3×D3×#99

Subgroups

subgroupG/H
centerC2D3×C22⋊C4×ΓL(1,𝔽8)
commutatorC22×C3×C7C22×C3×C4
FrattiniC23C22×D3×ΓL(1,𝔽8)
FittingC3×C7×#99C2×C3
socleC2×C3×C7C2×C3×C22⋊C4
prime radicalC2×D3×D4×ΓL(1,𝔽8)C2
cosocleC23×C3×C7C23×C3
hypercenter#99D3×ΓL(1,𝔽8)
hypocenterC3×C7C2×C3×#99
LCSG ▷ C22×C3×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C23 ◁ #99

892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#99×AGL(1,𝔽7), D3×ΓL(1,𝔽8)×B(4,𝔽2), D3×#89513⋊C3
maximal normal subgroup ofD3×#99×AGL(1,𝔽7), D3×ΓL(1,𝔽8)×B(4,𝔽2), D3×#89513⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.