Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | D3×C3⋊(C5⋊D115) |
| unambiguous semidirect product | (C3×D3)⋊(C5⋊D115) |
| unambiguous semidirect product | (C5×D3)⋊D345 |
| unambiguous semidirect product | (D3×C23)⋊(C3⋊(C5⋊D5)) |
| Fitting, socle, derived, Hall | C32×C52×C23 ⋊ C22 |
| Hall | C52×C23 ⋊ D32 |
| Hall | C32×C52 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ D3×D69 |
| Sylow | C23 ⋊ D3×C3⋊(C5⋊D5) |
| Sylow | C32 ⋊ C2×C5⋊D115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52×C23 | C22 |
| LCS | G ▷ C32×C52×C23 | |
| UCS | C1 | |
352 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 100 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, 320);