Finite Group DatabasebetaFinite Group Databasebeta| order | 5822 |
| automorphism | Aut(G) order 8150800 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2911 |
| unambiguous semidirect product | C41⋊D71 |
| unambiguous semidirect product | C71⋊D41 |
| Fitting, socle, derived, Hall | C41×C71 ⋊ C2 |
| Sylow | C71 ⋊ D41 |
| Sylow | C41 ⋊ D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C71 | C2 |
| LCS | G ▷ C41×C71 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,41,71|b^a=b^40,c^a=c^701457 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D41×D71, C2×D2911, C3×D2911, … |
| maximal normal subgroup of | D41×D71, C2×D2911, C3×D2911, … |
| maximal quotient of | Dic2911, C2×D2911, C3×D2911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5822, 3);