Finite Group DatabasebetaFinite Group Databasebeta| order | 4586 |
| automorphism | Aut(G) order 5255556 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2293 |
| unambiguous semidirect product | C2293⋊C2 |
| Fitting, socle, derived, Sylow | C2293 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C2293 | C2 |
| LCS | G ▷ C2293 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 2293 |
| transitive degree | μt(G) = 2293 |
Polycyclic presentation:
2,2293|b^a=b^22921148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D2293⋊C3, C3×D2293, D6879, … |
| maximal normal subgroup of | D2293⋊C3, C3×D2293, C5×D2293, … |
| maximal quotient of | C3×D2293, D6879, C5×D2293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4586, 1);