Finite Group Databasebeta

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AGL(1,𝔽7)×#3184 #72259589

order5376
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C27×C4

Aliases

direct productAGL(1,𝔽7)×#3184

Splittings

FittingC7×#3184 ⋊ C2×C3
HallD7×#3184 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#3184
SylowC7 ⋊ C2×C3×#3184

Subgroups

subgroupG/H
centerC22C22×D4×AGL(1,𝔽7)
commutator, cosocleC2×C4×C7C25×C3
FrattiniC2×C4C24×AGL(1,𝔽7)
FittingC7×#3184C2×C3
socleC22×C7C23×C3×D4
hypercenter#3184AGL(1,𝔽7)
hypocenterC7C2×C3×#3184
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3184

5028 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#19745
maximal normal subgroup ofAGL(1,𝔽7)×#19745

GAP

Past the SmallGroups library coverage — no SmallGroups id.