Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×#3952 |
| Fitting | C2×C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ C22⋊C8 |
122 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13100826, #13100827, #13100832, … |
| maximal normal subgroup of | #13100826, #13100827, #13100832, … |
| maximal quotient of | C5×#64679, C5×#64676, C5×#64688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 305);