Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of #67156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#67158 |
| Hall | C32×C52 ⋊ Q8 |
| Sylow | C52 ⋊ #627 |
| Sylow | C32 ⋊ C5×Dic10 |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | #72230610 |
| maximal normal subgroup of | #72230610 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 482);