Finite Group DatabasebetaFinite Group Databasebeta| order | 23137 |
| automorphism | ? |
| homology | Abelianization (H1) = C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1361⋊C17 |
| Fitting, socle, derived, Sylow | C1361 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1361 | C17 |
| LCS | G ▷ C1361 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
17,1361|b^a=b^26097 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23137, 1);