Finite Group DatabasebetaFinite Group Databasebeta| order | 7134 |
| automorphism | Aut(G) order 7990080 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3567 |
| unambiguous semidirect product | C3⋊D1189 |
| unambiguous semidirect product | C29⋊D123 |
| unambiguous semidirect product | C41⋊D87 |
| Fitting, socle, derived, Hall | C3×C29×C41 ⋊ C2 |
| Hall | C29×C41 ⋊ D3 |
| Hall | C3×C41 ⋊ D29 |
| Hall | C3×C29 ⋊ D41 |
| Sylow | C41 ⋊ D87 |
| Sylow | C29 ⋊ D123 |
| Sylow | C3 ⋊ D1189 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C29×C41 | C2 |
| LCS | G ▷ C3×C29×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,41|b^a=b^2,c^a=c^28,d^a=d^401785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D41×D87, D29×D123, D3×D1189, … |
| maximal normal subgroup of | D41×D87, D29×D123, D3×D1189, … |
| maximal quotient of | Dic3567, C2×D3567, D10701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7134, 8);