Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C5 |
| direct product | #41×#1044 |
| Fitting | C52×#41 ⋊ C4 |
| Sylow | C52 ⋊ C4×#41 |
784 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×#1044, #72220972, #72220978, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×#1044, #72220972, #72220978, … |
| maximal quotient of | #121×#1044 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10126);