Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #87831 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#87834 |
| Sylow | C52 ⋊ C2×M16 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | #13103289, #13104009, #13104011, … |
| maximal normal subgroup of | #13103289, #13104009, #13104011, … |
| maximal quotient of | #13103913, #13103919, #13103951, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1033);