Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22×C5 |
| direct product | C5×#87808 |
| Fitting | C2×C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22⋊C4 |
464 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
530 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 595);