Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D13×D67 |
| Fitting, Hall | C9×C13×C67 ⋊ C22 |
| derived, Hall | C13×C67 ⋊ C22×C9 |
| Hall | C9×C67 ⋊ C2×D13 |
| Hall | C9×C13 ⋊ C2×D67 |
| Sylow | C67 ⋊ C2×C9×D13 |
| Sylow | C13 ⋊ C2×C9×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D13×D67 |
| commutator, hypocenter | C13×C67 | C22×C9 |
| Frattini | C3 | C3×D13×D67 |
| Fitting | C9×C13×C67 | C22 |
| socle, cosocle | C3×C13×C67 | C22×C3 |
| prime radical | C3×D13×D67 | C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C9 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
2520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 52);