Finite Group DatabasebetaFinite Group Databasebeta| order | 23123 |
| automorphism | ? |
| homology | Abelianization (H1) = C19 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1217⋊C19 |
| Fitting, socle, derived, Sylow | C1217 ⋊ C19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1217 | C19 |
| LCS | G ▷ C1217 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
19,1217|b^a=b^47883 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23123, 1);