Finite Group DatabasebetaFinite Group Databasebeta| order | 10366 |
| automorphism | Aut(G) order 26122320 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5183 |
| unambiguous semidirect product | C71⋊D73 |
| unambiguous semidirect product | C73⋊D71 |
| Fitting, socle, derived, Hall | C71×C73 ⋊ C2 |
| Sylow | C73 ⋊ D71 |
| Sylow | C71 ⋊ D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C71×C73 | C2 |
| LCS | G ▷ C71×C73 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,71,73|b^a=b^70,c^a=c^722593 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D71×D73, C2×D5183, C3×D5183, … |
| maximal normal subgroup of | D71×D73, C2×D5183, C3×D5183, … |
| maximal quotient of | Dic5183, C2×D5183, C3×D5183, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10366, 3);