Finite Group Databasebeta

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AGL(1,𝔽7)×#63818 #72254170

order12096
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽7)×#63818

Splittings

HallC32×ΓL(1,𝔽8) ⋊ C22×M16
SylowC7 ⋊ C2×C3×#63818

Subgroups

subgroupG/H
center, FrattiniC4C2×D32×AGL(1,𝔽7)
commutator, socleC2×C32×C7C23×C3×C4
FittingC2×C32×C4×C7C23×C3
prime radicalC22×C3⋊D3×AGL(1,𝔽7)C4
cosocleC32×C4×C7C24×C3
hypercenterC2×C4D32×AGL(1,𝔽7)
hypocenterC32×C7C22×C3×M16
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C4 ◁ C2×C4

3236 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.