Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×C4⋊Dic5 |
| Sylow | C52 ⋊ C2×C4⋊C4 |
238 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13099333, #13099334, #13099337, … |
| maximal normal subgroup of | #13099333, #13099334, #13099337, … |
| maximal quotient of | C2×C5×C4⋊#168, C5×#65213, C4×C5×C4⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 818);