Finite Group DatabasebetaFinite Group Databasebeta| order | 15992 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1999⋊C8 |
| derived, Sylow | C1999 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D1999 |
| commutator, hypocenter | C1999 | C8 |
| Fitting, cosocle | C4×C1999 | C2 |
| socle, prime radical | C2×C1999 | C4 |
| LCS | G ▷ C1999 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15992 |
Polycyclic presentation:
2^3,1999|a^2=b,b^2=c,d^a=d^19984004 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D1999, C2×C1999⋊C8, #44544529, … |
| maximal normal subgroup of | C8×D1999, C2×C1999⋊C8, #44544529, … |
| maximal quotient of | C1999⋊C16, C2×C1999⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15992, 6);