Finite Group DatabasebetaFinite Group Databasebeta| order | 8418 |
| automorphism | Aut(G) order 11111760 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4209 |
| unambiguous semidirect product | C3⋊D1403 |
| unambiguous semidirect product | C23⋊D183 |
| unambiguous semidirect product | C61⋊D69 |
| Fitting, socle, derived, Hall | C3×C23×C61 ⋊ C2 |
| Hall | C23×C61 ⋊ D3 |
| Hall | C3×C61 ⋊ D23 |
| Hall | C3×C23 ⋊ D61 |
| Sylow | C61 ⋊ D69 |
| Sylow | C23 ⋊ D183 |
| Sylow | C3 ⋊ D1403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C23×C61 | C2 |
| LCS | G ▷ C3×C23×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,61|b^a=b^2,c^a=c^22,d^a=d^602106 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D69, D23×D183, D3×D1403, … |
| maximal normal subgroup of | D61×D69, D23×D183, D3×D1403, … |
| maximal quotient of | Dic4209, C2×D4209, D12627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8418, 9);