Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C49×D53 |
| unambiguous semidirect product | C53⋊(C22×C3×C49) |
| unambiguous semidirect product | (C2×C53)⋊(C2×C3×C49) |
| Fitting | C2×C3×C49×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C22×C3×C49 |
| Hall | C3×C49×C53 ⋊ C22 |
| Hall | C49×C53 ⋊ C22×C3 |
| Hall | C3×C53 ⋊ C22×C49 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15582 |
8232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 34);