Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87771 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#87773 |
| Sylow | C52 ⋊ C2×SD16 |
174 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #13100529, #13100530, C4×#87773, … |
| maximal normal subgroup of | #13100529, #13100530, C4×#87773, … |
| maximal quotient of | #13100448, #13100451, #13100467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 605);