Finite Group DatabasebetaFinite Group Databasebeta| order | 10614 |
| automorphism | Aut(G) order 17831520 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5307 |
| unambiguous semidirect product | C3⋊D1769 |
| unambiguous semidirect product | C29⋊D183 |
| unambiguous semidirect product | C61⋊D87 |
| Fitting, socle, derived, Hall | C3×C29×C61 ⋊ C2 |
| Hall | C29×C61 ⋊ D3 |
| Hall | C3×C61 ⋊ D29 |
| Hall | C3×C29 ⋊ D61 |
| Sylow | C61 ⋊ D87 |
| Sylow | C29 ⋊ D183 |
| Sylow | C3 ⋊ D1769 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C29×C61 | C2 |
| LCS | G ▷ C3×C29×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,61|b^a=b^2,c^a=c^28,d^a=d^602655 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D87, D29×D183, D3×D1769, … |
| maximal normal subgroup of | D61×D87, D29×D183, D3×D1769, … |
| maximal quotient of | Dic5307, C2×D5307, D15921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10614, 9);