Finite Group Databasebeta

← Prev (#13133538) Next (#13133540) →

3−1+2×C7⋊C9 #13133539

order1701
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×C7⋊C9

Splittings

SylowC7 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C32×ΓL(1,𝔽8)
commutatorC3×C7C32×C9
FittingC3×C7×3−1+2C3
socle, cosocleC32×C7C33
prime radicalC33×C7C32
hypercenterC3×3−1+2ΓL(1,𝔽8)
hypocenterC7C9×3−1+2
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C32 ◁ C3×3−1+2

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 567

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1701, 175);