Finite Group DatabasebetaFinite Group Databasebeta| order | 4526 |
| automorphism | Aut(G) order 4888080 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2263 |
| unambiguous semidirect product | C31⋊D73 |
| unambiguous semidirect product | C73⋊D31 |
| Fitting, socle, derived, Hall | C31×C73 ⋊ C2 |
| Sylow | C73 ⋊ D31 |
| Sylow | C31 ⋊ D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C73 | C2 |
| LCS | G ▷ C31×C73 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 104 |
| transitive degree | μt(G) = 2263 |
Polycyclic presentation:
2,31,73|b^a=b^30,c^a=c^721133 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2263, D6789, (C73⋊C3)⋊D31, … |
| maximal normal subgroup of | C3×D2263, (C73⋊C3)⋊D31, (C31⋊C3)⋊D73, … |
| maximal quotient of | C3×D2263, D6789, C5×D2263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4526, 3);