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#13133554

order1701
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

No aliases for this group.

Splittings

SylowC7 ⋊ #6893

Subgroups

subgroupG/H
center, FrattiniC32C32×ΓL(1,𝔽8)
commutator, socle, cosocleC32×C7C33
Fitting, prime radicalC3×C7×H(3,𝔽3)C3
hypercenterC3×H(3,𝔽3)ΓL(1,𝔽8)
hypocenterC7#6893
LCSG ▷ C32×C7 ▷ C7
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 567

Polycyclic presentation:

3^5,7|c^3=d,b^a=bd,c^a=ce,f^c=f^2

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 190);