Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C7×C92 ⋊ C3 |
| Sylow | C7 ⋊ #6897 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×ΓL(1,𝔽8) |
| commutator, socle, cosocle | C32×C7 | C33 |
| Fitting | C7×C92 | C3 |
| prime radical | C32×ΓL(1,𝔽8) | C32 |
| hypercenter | C92 | ΓL(1,𝔽8) |
| hypocenter | C7 | #6897 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ C92 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
3^5,7|b^3=de,c^3=d,b^a=bd,c^a=ce,f^a=f^2213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 214);