Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1725 |
| unambiguous semidirect product | (C3×D3)⋊D575 |
| unambiguous semidirect product | (D3×C23)⋊D75 |
| unambiguous semidirect product | (D3×C25)⋊D69 |
| Fitting, derived, Hall | C32×C23×C25 ⋊ C22 |
| Hall | C23×C25 ⋊ D32 |
| Hall | C32×C25 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×D25 |
| Sylow | C25 ⋊ D3×D69 |
| Sylow | C23 ⋊ D3×D75 |
| Sylow | C32 ⋊ C2×D575 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C23×C25 | C22 |
| Frattini | C5 | D3×D345 |
| socle | C32×C5×C23 | C2×D5 |
| LCS | G ▷ C32×C23×C25 | |
| UCS | C1 | |
132 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3450 |
2592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 83);