Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #87831 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#87831 |
| Sylow | C53 ⋊ C22⋊C4 |
196 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87831, C5×#11717375, #72259210 |
| maximal normal subgroup of | D5×#87831, C5×#11717375, #72259210 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 630);