Finite Group Databasebeta

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ΓL(1,𝔽8)×#10595100 #72269303

order12096
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productΓL(1,𝔽8)×#10595100

Splittings

FittingC2×C32×C7×D4 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C2×AGL(1,ℤ/8)
SylowC7 ⋊ C3×#10595100

Subgroups

subgroupG/H
centerC2C2×ΓL(1,𝔽8)×#3811
commutator, cosocleC32×C4×C7C24×C3
FrattiniC4C22×D32×ΓL(1,𝔽8)
FittingC2×C32×C7×D4C22×C3
socleC2×C32×C7C22×C3×D4
hypercenterC2×D4D32×ΓL(1,𝔽8)
hypocenterC32×C7C2×C3×AGL(1,ℤ/8)
LCSG ▷ C32×C4×C7 ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

3236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.