Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C5⋊D5×#4294⋊C2 |
| unambiguous semidirect product | (C5×#4294⋊C2)⋊D5 |
| derived, Hall | C52×C19 ⋊ C22×C9 |
| Hall | C52×#4294 ⋊ C22 |
| Hall | D19×C5⋊D5 ⋊ C9 |
| Hall | #4294 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×#4294⋊C2 |
| Sylow | C19 ⋊ C2×C9×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊D5×D19⋊C3 |
| commutator, hypocenter | C52×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C52×C19 | C22×C3 |
| prime radical | C3×D19×C5⋊D5 | C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4275 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 180);