Finite Group Databasebeta

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AGL(1,𝔽7)×#1790 #72277333

order5376
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽7)×#1790

Splittings

FittingC7×#1790 ⋊ C2×C3
HallD7×#1790 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#1790
SylowC7 ⋊ C2×C3×#1790

Subgroups

subgroupG/H
centerC22#120×AGL(1,𝔽7)
commutatorC23×C7C23×C3×C4
FrattiniC24C23×AGL(1,𝔽7)
FittingC7×#1790C2×C3
socleC22×C7C2×C3×#120
prime radicalC2×H(5,𝔽2)×AGL(1,𝔽7)C2
cosocleC24×C7C24×C3
hypercenter#1790AGL(1,𝔽7)
hypocenterC7C2×C3×#1790
LCSG ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ #1790

8804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 224

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.