Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3935 |
| Sylow | C52 ⋊ #97 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13099256, #13099257, #13099258, … |
| maximal normal subgroup of | #13099256, #13099257, #13099258, … |
| maximal quotient of | C5×#64674, C5×#64686, C5×#64744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 288);