Finite Group DatabasebetaFinite Group Databasebeta| order | 4582 |
| automorphism | Aut(G) order 5003544 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2291 |
| unambiguous semidirect product | C29⋊D79 |
| unambiguous semidirect product | C79⋊D29 |
| Fitting, socle, derived, Hall | C29×C79 ⋊ C2 |
| Sylow | C79 ⋊ D29 |
| Sylow | C29 ⋊ D79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C79 | C2 |
| LCS | G ▷ C29×C79 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 108 |
| transitive degree | μt(G) = 2291 |
Polycyclic presentation:
2,29,79|b^a=b^28,c^a=c^781147 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2291, D6873, C29⋊(D79⋊C3), … |
| maximal normal subgroup of | C3×D2291, C29⋊(D79⋊C3), C5×D2291, … |
| maximal quotient of | C3×D2291, D6873, C5×D2291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4582, 3);