Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C5×#3944 |
| Sylow | C52 ⋊ M32 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13099275, #13099276, #13099279, … |
| maximal normal subgroup of | #13099275, #13099276, #13099279, … |
| maximal quotient of | C5×#64681, C5×C4⋊#672, C5×C22⋊#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 297);