Finite Group DatabasebetaFinite Group Databasebeta| order | 4502 |
| automorphism | Aut(G) order 5064750 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2251 |
| unambiguous semidirect product | C2251⋊C2 |
| Fitting, socle, derived, Sylow | C2251 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2251 | C2 |
| LCS | G ▷ C2251 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 2251 |
| transitive degree | μt(G) = 2251 |
Polycyclic presentation:
2,2251|b^a=b^22501127 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D2251⋊C3, C3×D2251, D6753, … |
| maximal normal subgroup of | D2251⋊C3, C3×D2251, D2251⋊C5, … |
| maximal quotient of | C3×D2251, D6753, C5×D2251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4502, 1);