Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×(C7⋊C9)⋊D71 |
| unambiguous semidirect product | (C2×C7⋊C9)⋊D71 |
| unambiguous semidirect product | (C2×C71)⋊(D7⋊C9) |
| unambiguous semidirect product | (C2×D497)⋊C9 |
| derived, Hall | C7×C71 ⋊ C22×C9 |
| Hall | C7⋊C9×C71 ⋊ C22 |
| Hall | C2×D497 ⋊ C9 |
| Sylow | C71 ⋊ C2×D7⋊C9 |
| Hall | C7⋊C9 ⋊ C2×D71 |
| Sylow | C7 ⋊ C2×C9×D71 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8946 |
1092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 26);