Finite Group DatabasebetaFinite Group Databasebeta| order | 23988 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C1999⋊C3) |
| unambiguous semidirect product | C1999⋊A4 |
| Fitting, socle, derived, Hall | C22×C1999 ⋊ C3 |
| Sylow | C1999 ⋊ A4 |
| Sylow | C22 ⋊ C1999⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C1999 | C3 |
| LCS | G ▷ C22×C1999 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7996 |
Polycyclic presentation:
3,2^2,1999|b^a=c,c^a=bc,d^a=d^8082668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23988, 11);