Finite Group Databasebeta

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C3×#104×AGL(1,𝔽7) #72244629

order4032
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC3×#104×AGL(1,𝔽7)

Splittings

FittingC3×C7×#104 ⋊ C2×C3
HallD7×#104 ⋊ C32
HallC3×ΓL(1,𝔽8) ⋊ C2×#104
SylowC7 ⋊ C2×C32×#104

Subgroups

subgroupG/H
centerC3×C4D4×AGL(1,𝔽7)
commutatorC4×C7C22×C32×C4
FrattiniC2×C4C22×C3×AGL(1,𝔽7)
FittingC3×C7×#104C2×C3
socleC2×C3×C7C2×C3×C22⋊C4
prime radicalC3×#41×AGL(1,𝔽7)C2
cosocleC2×C4×C7C23×C32
hypercenterC3×#104AGL(1,𝔽7)
hypocenterC7C2×C32×#104
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#104

1020 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

294 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×#453, #104×ΓL(1,𝔽8)⋊AGL(1,𝔽7), D3×#104×AGL(1,𝔽7), …
maximal normal subgroup ofC3×AGL(1,𝔽7)×#453, D3×#104×AGL(1,𝔽7), AGL(1,𝔽7)×#4822
maximal quotient of#104×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.