Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#11717337 |
| unambiguous semidirect product | D5⋊#4039 |
| Fitting | C2×C4×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×C4×D4 |
879 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 879 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4×D5×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×D4×D5×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9966);