Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×#1043 |
| Fitting | C52×#41 ⋊ C4 |
| Sylow | C52 ⋊ C4×#41 |
1240 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/8)×#1043, #72220814, C2×#41×#1043, … |
| maximal normal subgroup of | AGL(1,ℤ/8)×#1043, #72220814, C2×#41×#1043, … |
| maximal quotient of | C4×D4×#1043, C2×#41×#1043, #72220975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10105);