Finite Group DatabasebetaFinite Group Databasebeta| order | 6058 |
| automorphism | Aut(G) order 8432736 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3029 |
| unambiguous semidirect product | C13⋊D233 |
| unambiguous semidirect product | C233⋊D13 |
| Fitting, socle, derived, Hall | C13×C233 ⋊ C2 |
| Sylow | C233 ⋊ D13 |
| Sylow | C13 ⋊ D233 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C233 | C2 |
| LCS | G ▷ C13×C233 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,233|b^a=b^12,c^a=c^2321516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27131125, #27131126, D13×D233, … |
| maximal normal subgroup of | #27131125, #27131126, D13×D233, … |
| maximal quotient of | Dic3029, C2×D3029, C3×D3029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6058, 3);