Finite Group DatabasebetaFinite Group Databasebeta| order | 15987 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5329⋊C3 |
| Fitting, derived, Sylow | C5329 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5329 | C3 |
| Frattini, socle | C73 | C73⋊C3 |
| LCS | G ▷ C5329 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5329 |
Polycyclic presentation:
3,73^2|b^73=c,b^a=b^8c^30,c^a=c^81779 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5329⋊C3, C2×C5329⋊C3 |
| maximal normal subgroup of | D5329⋊C3, C2×C5329⋊C3 |
| maximal quotient of | C2×C5329⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15987, 1);