Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C4×C5×#997 |
| Fitting, Hall | C4×C5×H(5,𝔽2) ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C3×C4×C5 |
| Sylow | C4×H(5,𝔽2) ⋊ C3×C5 |
690 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237080);