Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×#685 |
| Fitting | C2×C4×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×C22⋊C4 |
298 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #13103609, #13103618, #13103619, … |
| maximal normal subgroup of | #13103609, #13103618, #13103619, … |
| maximal quotient of | D5×#3937, #13100573, D5×#3938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 697);