Finite Group DatabasebetaFinite Group Databasebeta| order | 8418 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D69 |
| unambiguous semidirect product | C3⋊(D23×C61) |
| unambiguous semidirect product | C23⋊(D3×C61) |
| Fitting, socle, Hall | C3×C23×C61 ⋊ C2 |
| derived, Hall | C3×C23 ⋊ C2×C61 |
| Hall | C23×C61 ⋊ D3 |
| Hall | C3×C61 ⋊ D23 |
| Sylow | C23 ⋊ D3×C61 |
| Sylow | C3 ⋊ D23×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D69 |
| commutator, hypocenter | C3×C23 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C61 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C61 | |
16 conjugacy classes of subgroups.
2196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D69, D3×D23×C61, D69⋊D61, … |
| maximal normal subgroup of | D61×D69, D3×D23×C61, D69⋊D61, … |
| maximal quotient of | C61×Dic69, C2×C61×D69, C61×D207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8418, 8);