Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic25 |
| Sylow | C25 ⋊ C4×D4 |
141 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#6016, #13098031, #13098034, … |
| maximal normal subgroup of | D4⋊#6016, #13098031, #13098034, … |
| maximal quotient of | C22⋊C4×Dic25, #13098223, #13098224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 155);