Finite Group Databasebeta

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AGL(1,𝔽7)×#3025 #72277740

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

Aliases

direct productAGL(1,𝔽7)×#3025

Splittings

FittingC7×#3025 ⋊ C2×C3
HallD7×#3025 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#3025
SylowC7 ⋊ C2×C3×#3025

Subgroups

subgroupG/H
centerC4#120×AGL(1,𝔽7)
commutator, cosocleC23×C7C25×C3
FrattiniC23C24×AGL(1,𝔽7)
FittingC7×#3025C2×C3
socleC2×C7C22×C3×#120
hypercenter#3025AGL(1,𝔽7)
hypocenterC7C2×C3×#3025
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C4 ◁ C22×C4 ◁ #3025

10172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.