Finite Group Databasebeta

← Prev (#72244157) Next (#72244159) →

AGL(1,𝔽7)×#937 #72244158

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

Aliases

direct productAGL(1,𝔽7)×#937

Splittings

FittingC2×C3×C7×D4 ⋊ C22×C3
HallC3×ΓL(1,𝔽8) ⋊ C2×#120
SylowC7 ⋊ C2×C3×#937

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽7)
commutator, socle, cosocleC22×C3×C7C24×C3
FittingC2×C3×C7×D4C22×C3
hypercenterC2×D4D3×AGL(1,𝔽7)
hypocenterC3×C7C2×C3×#120
LCSG ▷ C22×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×D4

2884 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#120×AGL(1,𝔽7), AGL(1,𝔽7)×#5244, AGL(1,𝔽7)×#4741, …
maximal normal subgroup ofD3×#120×AGL(1,𝔽7), AGL(1,𝔽7)×#5244, AGL(1,𝔽7)×#4741
maximal quotient ofAGL(1,𝔽7)×#5077, AGL(1,𝔽7)×#5032, AGL(1,𝔽7)×#5198, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.