Finite Group DatabasebetaFinite Group Databasebeta| order | 8722 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D49 |
| unambiguous semidirect product | C49⋊(C2×C89) |
| Fitting, Hall | C49×C89 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D49 |
| commutator, hypocenter | C49 | C2×C89 |
| Frattini | C7 | D7×C89 |
| Fitting | C49×C89 | C2 |
| socle | C7×C89 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C89 | |
12 conjugacy classes of subgroups.
2314 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×D89, C2×C89×D49, C3×C89×D49, … |
| maximal normal subgroup of | D49×D89, C2×C89×D49, C3×C89×D49, … |
| maximal quotient of | C89×Dic49, C2×C89×D49, C3×C89×D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8722, 2);