Finite Group DatabasebetaFinite Group Databasebeta| order | 17316 |
| isoclinism | isoclinic class of #66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2 |
| direct product | C22×C13×#66526 |
| Fitting, socle, Hall | C22×C13×C37 ⋊ C9 |
| derived, Sylow | C37 ⋊ C22×C9×C13 |
| Hall | C13×C37 ⋊ C22×C9 |
| Hall | C22×C37 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | #66526 |
| commutator, hypocenter | C37 | C22×C9×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C37 | C9 |
| prime radical | C22×C13×C37⋊C3 | C3 |
| cosocle | C37⋊C3 | C22×C3×C13 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C22×C13 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1924 |
676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17316, 278);