Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C5 |
| direct product | SD16×#1044 |
| Fitting | C52×SD16 ⋊ C4 |
| Sylow | C52 ⋊ C4×SD16 |
312 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D5⋊AGL(1,𝔽5), #72220853, #72220864, … |
| maximal normal subgroup of | SD16×D5⋊AGL(1,𝔽5), #72220853, #72220864, … |
| maximal quotient of | #106×#1044, #72242603 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7224);