Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#65362 |
| Fitting | C52×#127 ⋊ C2 |
| Sylow | C52 ⋊ #493 |
432 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #72221318, C5×#10612013, #72223452, … |
| maximal normal subgroup of | #72221318, C5×#10612013, #72223452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4685);