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C2×C3×C7⋊H(3,𝔽3) #11765768

order1134
isoclinismisoclinic class of #4427
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C34

Aliases

direct productC2×C3×C7⋊H(3,𝔽3)
unambiguous semidirect product(C2×C3×C7)⋊H(3,𝔽3)

Splittings

FittingC2×C33×C7 ⋊ C3
HallC2×C7 ⋊ C3×H(3,𝔽3)
SylowC7 ⋊ C2×C3×H(3,𝔽3)

Subgroups

subgroupG/H
centerC2×C32C3×ΓL(1,𝔽8)
commutator, cosocleC3×C7C2×C33
FrattiniC3C2×C32×ΓL(1,𝔽8)
FittingC2×C33×C7C3
socleC2×C32×C7C32
hypercenterC2×C33ΓL(1,𝔽8)
hypocenterC7C2×C3×H(3,𝔽3)
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C2×C32 ◁ C2×C33

224 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, 198);