Finite Group Databasebeta

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AGL(1,𝔽7)×#3021 #72278145

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

Aliases

direct productAGL(1,𝔽7)×#3021

Splittings

FittingC7×#3021 ⋊ C2×C3
HallD7×#3021 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#3021
SylowC7 ⋊ C2×C3×#3021

Subgroups

subgroupG/H
centerC2C2×#120×AGL(1,𝔽7)
commutator, cosocleC2×C4×C7C25×C3
FrattiniC2×C4C24×AGL(1,𝔽7)
FittingC7×#3021C2×C3
socleC2×C7C22×C3×#120
hypercenter#3021AGL(1,𝔽7)
hypocenterC7C2×C3×#3021
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C22×C4 ◁ #3021

9868 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.