Finite Group DatabasebetaFinite Group Databasebeta| order | 5998 |
| automorphism | Aut(G) order 8991002 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2999 |
| unambiguous semidirect product | C2999⋊C2 |
| Fitting, socle, derived, Sylow | C2999 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2999 | C2 |
| LCS | G ▷ C2999 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,2999|b^a=b^29981501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D2999, C3×D2999, D8997, … |
| maximal normal subgroup of | C2×D2999, C3×D2999, C5×D2999 |
| maximal quotient of | Dic2999, C2×D2999, C3×D2999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5998, 1);