Finite Group Databasebeta

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AGL(1,𝔽7)×#64306 #72247207

order12096
automorphism?
homologyAbelianization (H1) = C25×C3 · Schur multiplier (H2) = C29

Aliases

direct productAGL(1,𝔽7)×#64306

Splittings

FittingC2×C32×C4×C7 ⋊ C23×C3
HallC32×ΓL(1,𝔽8) ⋊ C22×#41
SylowC7 ⋊ C2×C3×#64306

Subgroups

subgroupG/H
centerC4C2×D32×AGL(1,𝔽7)
commutator, socle, cosocleC2×C32×C7C25×C3
FrattiniC2C22×D32×AGL(1,𝔽7)
FittingC2×C32×C4×C7C23×C3
hypercenterC2×C4D32×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×#41
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C4 ◁ C2×C4

8356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.