Finite Group DatabasebetaFinite Group Databasebeta| order | 8722 |
| isoclinism | isoclinic class of D89 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D89 |
| unambiguous semidirect product | C89⋊(C2×C49) |
| Fitting, Hall | C49×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D89 |
| commutator, hypocenter | C89 | C2×C49 |
| Frattini | C7 | C7×D89 |
| Fitting | C49×C89 | C2 |
| socle | C7×C89 | C2×C7 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C49 | |
12 conjugacy classes of subgroups.
2254 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#67063, C49⋊#67063, D49×D89, … |
| maximal normal subgroup of | C49×#67063, C49⋊#67063, D49×D89, … |
| maximal quotient of | C49×Dic89, C2×C49×D89, C3×C49×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8722, 3);