Finite Group DatabasebetaFinite Group Databasebeta| order | 15992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D1999 |
| Fitting | C22×C1999 ⋊ C2 |
| Sylow | C1999 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1999 |
| commutator, socle, cosocle | C2×C1999 | C22 |
| Fitting | C22×C1999 | C2 |
| hypercenter | C22 | D1999 |
| hypocenter | C1999 | D4 |
| LCS | G ▷ C2×C1999 ▷ C1999 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7996 |
Polycyclic presentation:
2^3,1999|b^a=bc,d^b=d^19984001 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×D1999, C2×C22⋊D1999, #44544545, … |
| maximal normal subgroup of | D4×D1999, C2×C22⋊D1999, #44544545, … |
| maximal quotient of | (C2×D1999)⋊C4, C22⋊Dic1999, Dic1999⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15992, 9);