Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×D5×#4294⋊C2 |
| unambiguous semidirect product | (C5×#4294⋊C2)⋊(C2×C5) |
| unambiguous semidirect product | (D5×#4294)⋊(C2×C5) |
| unambiguous semidirect product | (C5⋊(#4294⋊C2))⋊(C2×C5) |
| derived | C5×C19 ⋊ C22×C5×C9 |
| Hall | C52×#4294 ⋊ C22 |
| Hall | C5×D5×D19 ⋊ C9 |
| Hall | C52×C19 ⋊ C22×C9 |
| Hall | #4294 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×#4294⋊C2 |
| Sylow | C19 ⋊ C2×C5×C9×D5 |
144 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1710 |
540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 173);