Finite Group Databasebeta

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ΓL(1,𝔽8)×#10596675 #72269471

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

Aliases

direct productΓL(1,𝔽8)×#10596675

Splittings

FittingC2×C32×C7×D4 ⋊ C22×C3
HallC32×ΓL(1,𝔽8) ⋊ C2×H(5,𝔽2)
SylowC7 ⋊ C3×#10596675

Subgroups

subgroupG/H
center, FrattiniC2C23×D32×ΓL(1,𝔽8)
commutator, socle, cosocleC2×C32×C7C25×C3
FittingC2×C32×C7×D4C22×C3
hypercenterC2×D4D32×ΓL(1,𝔽8)
hypocenterC32×C7C2×C3×H(5,𝔽2)
LCSG ▷ C2×C32×C7 ▷ C32×C7
UCSC1 ◁ C2 ◁ C2×D4

8428 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.