Finite Group Databasebeta

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AGL(1,𝔽7)×#3026 #72277226

order5376
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C210

Aliases

direct productAGL(1,𝔽7)×#3026

Splittings

FittingC7×#3026 ⋊ C2×C3
HallD7×#3026 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#3026
SylowC7 ⋊ C2×C3×#3026

Subgroups

subgroupG/H
centerC2C2×#120×AGL(1,𝔽7)
commutator, cosocleC23×C7C25×C3
FrattiniC23C24×AGL(1,𝔽7)
FittingC7×#3026C2×C3
socleC2×C7C22×C3×#120
hypercenter#3026AGL(1,𝔽7)
hypocenterC7C2×C3×#3026
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C24 ◁ #3026

10636 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.