Finite Group DatabasebetaFinite Group Databasebeta| order | 17316 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#16864526 |
| derived, Hall | C13×C37 ⋊ C22×C9 |
| Hall | C22×C13×C37 ⋊ C9 |
| Hall | C22×C37 ⋊ C13⋊C9 |
| Hall | C22×C13 ⋊ #66524 |
| Sylow | C37 ⋊ C22×C13⋊C9 |
| Sylow | C13 ⋊ C22×#66524 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #13089650 |
| commutator, hypocenter | C13×C37 | C22×C9 |
| Frattini | C3 | C22×#13089650 |
| Fitting, socle, prime radical | C22×C3×C13×C37 | C3 |
| cosocle | C3×C13×C37 | C22×C3 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C22×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17316 |
1956 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17316, 87);