Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C2×#11717231 |
| Fitting | C2×C52×D8 ⋊ C2 |
| Sylow | C52 ⋊ C2×AGL(1,ℤ/8) |
1192 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,ℤ/8)×C5⋊D5, #72220973, #72220976, … |
| maximal normal subgroup of | C2×AGL(1,ℤ/8)×C5⋊D5, #72220973, #72220976, … |
| maximal quotient of | #72220976, #72223076, #72223081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9635);