Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#87718 |
| Sylow | C25 ⋊ C2×C4⋊C4 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097673, #13097900, #13097904, … |
| maximal normal subgroup of | #13097673, #13097900, #13097904, … |
| maximal quotient of | C4×#87718, #13098209, #13098217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 144);