Finite Group DatabasebetaFinite Group Databasebeta| order | 10126 |
| automorphism | Aut(G) order 24909960 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5063 |
| unambiguous semidirect product | C61⋊D83 |
| unambiguous semidirect product | C83⋊D61 |
| Fitting, socle, derived, Hall | C61×C83 ⋊ C2 |
| Sylow | C83 ⋊ D61 |
| Sylow | C61 ⋊ D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C83 | C2 |
| LCS | G ▷ C61×C83 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,61,83|b^a=b^60,c^a=c^822533 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D83, C2×D5063, C3×D5063, … |
| maximal normal subgroup of | D61×D83, C2×D5063, C3×D5063, … |
| maximal quotient of | Dic5063, C2×D5063, C3×D5063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10126, 3);