Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C4×C5×C22⋊D5 |
| Fitting | C22×C4×C52 ⋊ C2 |
| Sylow | C52 ⋊ C4×D4 |
242 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 242 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) = 80 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #168×C22⋊D5, #13101488, #13101491, … |
| maximal normal subgroup of | #168×C22⋊D5, #13101488, #13101491, … |
| maximal quotient of | C4×C5×#683, C5×#65222, C4×C5×#685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 821);