Finite Group Databasebeta

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AGL(1,𝔽7)×#1795 #72277084

order5376
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C28

Aliases

direct productAGL(1,𝔽7)×#1795

Splittings

FittingC7×#1795 ⋊ C2×C3
HallD7×#1795 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#1795
SylowC7 ⋊ C2×C3×#1795

Subgroups

subgroupG/H
centerC2AGL(1,𝔽7)×#379
commutatorC2×C4×C7C23×C3×C4
FrattiniC22×C4C23×AGL(1,𝔽7)
FittingC7×#1795C2×C3
socleC2×C7C2×C3×#379
prime radicalC2×H(5,𝔽2)×AGL(1,𝔽7)C2
cosocleC22×C4×C7C24×C3
hypercenter#1795AGL(1,𝔽7)
hypocenterC7C2×C3×#1795
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C22×C4 ◁ #1795

7892 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.