Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1725 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D575) |
| unambiguous semidirect product | (C2×C23)⋊(C3×D75) |
| unambiguous semidirect product | (C2×C25)⋊(C3×D69) |
| Fitting | C2×C32×C23×C25 ⋊ C2 |
| derived | C3×C23×C25 ⋊ C22×C3 |
| Hall | C32×C23×C25 ⋊ C22 |
| Hall | C23×C25 ⋊ C2×C3×D3 |
| Hall | C32×C25 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C3×D69 |
| Sylow | C23 ⋊ C2×C3×D75 |
| Sylow | C32 ⋊ C2×D575 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1725 |
| commutator, cosocle, hypocenter | C3×C23×C25 | C22×C3 |
| Frattini | C5 | C2×C3×D345 |
| Fitting | C2×C32×C23×C25 | C2 |
| socle | C2×C32×C5×C23 | D5 |
| LCS | G ▷ C3×C23×C25 | |
| UCS | C1 ◁ C2×C3 | |
132 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6900 |
5184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 100);