Finite Group DatabasebetaFinite Group Databasebeta| order | 4913 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C172 · Schur multiplier (H2) = C172 |
| unitriangular | UT(3,𝔽17) |
| extraspecial | 17+1+2 |
| Heisenberg | H(3,𝔽17) |
| unambiguous semidirect product | C172⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle | C17 | C172 |
| LCS | G ▷ C17 ▷ C1 | |
| UCS | C1 ◁ C17 ◁ G | |
| LECS | G ▷ C17 ▷ C1 | |
39 conjugacy classes of subgroups.
Polycyclic presentation:
17^3|b^a=bc305 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4913, 3);