Finite Group Databasebeta

← Prev (#72249145) Next (#72249147) →

AGL(1,𝔽7)×#6891 #72249146

order10206
automorphism?
homologyAbelianization (H1) = C2×C34 · Schur multiplier (H2) = C36

Aliases

direct productAGL(1,𝔽7)×#6891

Splittings

FittingC7×#6891 ⋊ C2×C3
HallΓL(1,𝔽8)×#6891 ⋊ C2
HallD7 ⋊ C3×#6891
SylowC7 ⋊ C2×C3×#6891

Subgroups

subgroupG/H
center, FrattiniC32C33×AGL(1,𝔽7)
commutator, socle, cosocleC32×C7C2×C34
FittingC7×#6891C2×C3
prime radicalC34×AGL(1,𝔽7)C3
hypercenter#6891AGL(1,𝔽7)
hypocenterC7C2×C3×#6891
LCSG ▷ C32×C7 ▷ C7
UCSC1 ◁ C32 ◁ #6891

5272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 189

Conjugacy classes & character table

357 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#10624749, AGL(1,𝔽7)×#92302
maximal normal subgroup ofAGL(1,𝔽7)×#10624749, AGL(1,𝔽7)×#92302

GAP

Past the SmallGroups library coverage — no SmallGroups id.