Finite Group DatabasebetaFinite Group Databasebeta| order | 23097 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7699⋊C3 |
| Fitting, socle, derived, Sylow | C7699 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7699 | C3 |
| LCS | G ▷ C7699 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7699 |
Polycyclic presentation:
3,7699|b^a=b^22692569 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23097, 1);