Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | SD32×C5⋊D5 |
| Fitting | C52×SD32 ⋊ C2 |
| Sylow | C52 ⋊ C2×SD32 |
360 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#509, SD32×#1043, #72242337, … |
| maximal normal subgroup of | C5⋊D5×#509, SD32×#1043, #72242337, … |
| maximal quotient of | C5⋊D5×#357, C5⋊D5×#367, C2×SD32×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5128);