Finite Group DatabasebetaFinite Group Databasebeta| order | 5006 |
| automorphism | Aut(G) order 6262506 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2503 |
| unambiguous semidirect product | C2503⋊C2 |
| Fitting, socle, derived, Sylow | C2503 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2503 | C2 |
| LCS | G ▷ C2503 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,2503|b^a=b^25021253 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D2503⋊C3, C3×D2503, D7509, … |
| maximal normal subgroup of | D2503⋊C3, C3×D2503, C5×D2503, … |
| maximal quotient of | C3×D2503, D7509, C5×D2503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5006, 1);