Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#87720 |
| Fitting | C22×C4×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×C22⋊C4 |
198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #13097675, #13097902, #13097905, … |
| maximal normal subgroup of | #13097675, #13097902, #13097905, … |
| maximal quotient of | C2×#11716353, #13098203, C4×#87720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 148);