Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#3932 |
| Fitting | C52×C16 ⋊ C2 |
| Sylow | C52 ⋊ SD32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
215 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3932, #13100413, #13100415, … |
| maximal normal subgroup of | D5×#3932, #13100413, #13100415, … |
| maximal quotient of | C5×#64725, C5×#64729, C5×#64723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 285);