Finite Group DatabasebetaFinite Group Databasebeta| order | 8642 |
| automorphism | Aut(G) order 17906224 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4321 |
| unambiguous semidirect product | C29⋊D149 |
| unambiguous semidirect product | C149⋊D29 |
| Fitting, socle, derived, Hall | C29×C149 ⋊ C2 |
| Sylow | C149 ⋊ D29 |
| Sylow | C29 ⋊ D149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C149 | C2 |
| LCS | G ▷ C29×C149 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,29,149|b^a=b^28,c^a=c^1482162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31772227, #31772228, D29×D149, … |
| maximal normal subgroup of | #31772227, #31772228, D29×D149, … |
| maximal quotient of | Dic4321, C2×D4321, C3×D4321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8642, 3);