Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#3941 |
| Fitting | C52×C4⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ #102 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13100606, #13100608, #13100610, … |
| maximal normal subgroup of | #13100606, #13100608, #13100610, … |
| maximal quotient of | C5×#64671, C5×#64703, C5×#64705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 294);