Finite Group DatabasebetaFinite Group Databasebeta| order | 28322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D49×C289 |
| unambiguous semidirect product | C49⋊(C2×C289) |
| Fitting, Hall | C49×C289 ⋊ C2 |
| derived, Sylow | C49 ⋊ C2×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D49 |
| commutator, hypocenter | C49 | C2×C289 |
| Frattini, socle | C7×C17 | D7×C17 |
| Fitting | C49×C289 | C2 |
| prime radical | C17×D49 | C17 |
| cosocle | C17×C49 | C2×C17 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C289 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14161 |
7514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28322, 2);