Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D9×D23 |
| unambiguous semidirect product | (D9×C23)⋊(C2×C52) |
| unambiguous semidirect product | (C9×D23)⋊(C2×C52) |
| unambiguous semidirect product | D207⋊(C2×C52) |
| Fitting, Hall | C52×C9×C23 ⋊ C22 |
| derived, Hall | C9×C23 ⋊ C22×C52 |
| Hall | C52×C23 ⋊ C2×D9 |
| Hall | C52×C9 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C52×D9 |
| Sylow | C9 ⋊ C2×C52×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D9×D23 |
| commutator, cosocle, hypocenter | C9×C23 | C22×C52 |
| Frattini | C3 | C52×D3×D23 |
| Fitting | C52×C9×C23 | C22 |
| socle | C3×C52×C23 | C2×D3 |
| LCS | G ▷ C9×C23 | |
| UCS | C1 ◁ C52 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5175 |
1950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 135);