Finite Group DatabasebetaFinite Group Databasebeta| order | 20700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×(C3⋊D3)⋊D115 |
| unambiguous semidirect product | (C3⋊D3)⋊(C5×D115) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C22 |
| derived | C32×C5×C23 ⋊ C22×C5 |
| Hall | C52×C23 ⋊ D32 |
| Hall | C32×C52 ⋊ C2×D23 |
| Hall | C32×C23 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ (C3⋊D3)⋊D23 |
| Sylow | C23 ⋊ C5×(C3⋊D3)⋊D5 |
| Sylow | C32 ⋊ C2×C5×D115 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (C3⋊D3)⋊D115 |
| commutator, cosocle, hypocenter | C32×C5×C23 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C22 |
| LCS | G ▷ C32×C5×C23 | |
| UCS | C1 ◁ C5 | |
224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 690 |
1755 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20700, 311);