Finite Group DatabasebetaFinite Group Databasebeta| order | 9998 |
| automorphism | Aut(G) order 24985002 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4999 |
| unambiguous semidirect product | C4999⋊C2 |
| Fitting, socle, derived, Sylow | C4999 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C4999 | C2 |
| LCS | G ▷ C4999 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4999|b^a=b^49982501 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4999, D4999⋊C3, C3×D4999, … |
| maximal normal subgroup of | C2×D4999, D4999⋊C3, C3×D4999 |
| maximal quotient of | Dic4999, C2×D4999, C3×D4999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9998, 1);