Finite Group Databasebeta

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C3×#99×AGL(1,𝔽7) #72246158

order4032
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3

Aliases

direct productC3×#99×AGL(1,𝔽7)

Splittings

FittingC3×C7×#99 ⋊ C2×C3
HallD7×#99 ⋊ C32
HallC3×ΓL(1,𝔽8) ⋊ C2×#99
SylowC7 ⋊ C2×C32×#99

Subgroups

subgroupG/H
centerC2×C3C22⋊C4×AGL(1,𝔽7)
commutatorC22×C7C22×C32×C4
FrattiniC23C22×C3×AGL(1,𝔽7)
FittingC3×C7×#99C2×C3
socleC2×C3×C7C2×C3×C22⋊C4
prime radicalC2×C3×D4×AGL(1,𝔽7)C2
cosocleC23×C7C23×C32
hypercenterC3×#99AGL(1,𝔽7)
hypocenterC7C2×C32×#99
LCSG ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C3×#99

1260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×B(4,𝔽2), #99×ΓL(1,𝔽8)⋊AGL(1,𝔽7), D3×#99×AGL(1,𝔽7), …
maximal normal subgroup ofC3×AGL(1,𝔽7)×B(4,𝔽2), D3×#99×AGL(1,𝔽7), AGL(1,𝔽7)×#4741
maximal quotient of#99×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.