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C9×C7⋊H(3,𝔽3) #13133532

order1701
isoclinismisoclinic class of #4427
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC9×C7⋊H(3,𝔽3)

Splittings

FittingC32×C7×C9 ⋊ C3
SylowC7 ⋊ C9×H(3,𝔽3)

Subgroups

subgroupG/H
centerC3×C9C3×ΓL(1,𝔽8)
commutatorC3×C7C32×C9
FrattiniC32C32×ΓL(1,𝔽8)
FittingC32×C7×C9C3
socle, cosocleC32×C7C33
prime radicalC3×C7⋊H(3,𝔽3)C3
hypercenterC32×C9ΓL(1,𝔽8)
hypocenterC7C9×H(3,𝔽3)
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C3×C9 ◁ C32×C9

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 567

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 168);