Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#65373 |
| Fitting | C52×C4⋊Q8 ⋊ C2 |
| Sylow | C52 ⋊ #476 |
284 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
235 conjugacy classes — view the full character table.
| maximal subgroup of | #72223134 |
| maximal normal subgroup of | #72223134 |
| maximal quotient of | C5×#10602143 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4703);