Finite Group DatabasebetaFinite Group Databasebeta| order | 5988 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic499 |
| derived, Sylow | C499 ⋊ C3×C4 |
| Hall | C3×C499 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D499 |
| commutator, hypocenter | C499 | C3×C4 |
| Frattini | C2 | C3×D499 |
| Fitting, socle | C2×C3×C499 | C2 |
| LCS | G ▷ C499 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
1506 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic499⋊C9, C9×Dic499, C3×(C499⋊C3)⋊C4, … |
| maximal normal subgroup of | Dic499⋊C9, C9×Dic499, C3×(C499⋊C3)⋊C4, … |
| maximal quotient of | C9×Dic499, C32×Dic499, C3×Dic1497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5988, 5);