Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D5×D115 |
| unambiguous semidirect product | (C5×D5)⋊(C9×D23) |
| unambiguous semidirect product | (D5×C23)⋊(C9×D5) |
| Fitting, Hall | C52×C9×C23 ⋊ C22 |
| derived, Hall | C52×C23 ⋊ C22×C9 |
| Hall | C52×C9 ⋊ C2×D23 |
| Hall | C9×C23 ⋊ D52 |
| Sylow | C52 ⋊ C2×C9×D23 |
| Sylow | C23 ⋊ C9×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D5×D115 |
| commutator, hypocenter | C52×C23 | C22×C9 |
| Frattini | C3 | C3×D5×D115 |
| Fitting | C52×C9×C23 | C22 |
| socle, cosocle | C3×C52×C23 | C22×C3 |
| prime radical | C3×D5×D115 | C3 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C9 | |
144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2070 |
2124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 133);