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C2×(C3×ΓL(1,𝔽8))⋊C9 #11765640

order1134
automorphism?
homologyAbelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32

Aliases

direct productC2×(C3×ΓL(1,𝔽8))⋊C9
unambiguous semidirect product(C2×C3×ΓL(1,𝔽8))⋊C9

Splittings

FittingC2×C3×C7×C9 ⋊ C3
HallC2×C7 ⋊ C32⋊C9
SylowC7 ⋊ C2×C32⋊C9

Subgroups

subgroupG/H
centerC2×C32C3×ΓL(1,𝔽8)
commutatorC3×C7C2×C3×C9
FrattiniC32C2×C3×ΓL(1,𝔽8)
FittingC2×C3×C7×C9C3
socleC2×C32×C7C32
prime radicalC2×C32×ΓL(1,𝔽8)C3
cosocleC32×C7C2×C32
hypercenterC2×C3×C9ΓL(1,𝔽8)
hypocenterC7C2×C32⋊C9
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C2×C32 ◁ C2×C3×C9

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 378

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 70);