Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C5⋊(#4294⋊C2) |
| unambiguous semidirect product | (C2×C5)⋊(C5×#4294⋊C2) |
| unambiguous semidirect product | (C2×#4294)⋊(C5×D5) |
| derived | C5×C19 ⋊ C22×C5×C9 |
| Hall | C52×#4294 ⋊ C22 |
| Hall | C2×C5×D95 ⋊ 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 58 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3420 |
810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 197);