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3−1+2×C22⋊ΓL(1,𝔽8) #72277992

order2268
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C2×C32

Aliases

direct product3−1+2×C22⋊ΓL(1,𝔽8)

Splittings

FittingC22×C7×3−1+2 ⋊ C3
HallC22×C7 ⋊ C3×3−1+2
SylowC7 ⋊ A4×3−1+2
SylowC22 ⋊ ΓL(1,𝔽8)×3−1+2

Subgroups

subgroupG/H
center, FrattiniC3C32×C22⋊ΓL(1,𝔽8)
commutator, socle, cosocleC22×C3×C7C33
FittingC22×C7×3−1+2C3
prime radicalC32×C22⋊ΓL(1,𝔽8)C3
hypercenter3−1+2C22⋊ΓL(1,𝔽8)
hypocenterC22×C7C3×3−1+2
LCSG ▷ C22×C3×C7 ▷ C22×C7
UCSC1 ◁ C3 ◁ 3−1+2

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 252

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.