Finite Group DatabasebetaFinite Group Databasebeta| order | 1701 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C7 ⋊ #6894 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×ΓL(1,𝔽8) |
| commutator, socle, cosocle | C32×C7 | C33 |
| Fitting | C32×C7×C9 | C3 |
| prime radical | C33×C7 | C32 |
| hypercenter | C32×C9 | ΓL(1,𝔽8) |
| hypocenter | C7 | #6894 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ C32×C9 | |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
3^5,7|a^3=e,b^3=d,b^a=bd,c^a=ce,f^a=f^4213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1701, 200);