Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#3963 |
| Sylow | C52 ⋊ #95 |
206 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #13099319, #13099321, #13099323, … |
| maximal normal subgroup of | #13099319, #13099321, #13099323, … |
| maximal quotient of | C5×#64743, C5×#64744, C5×#64746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 316);