Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×C9×Dic10 |
| unambiguous semidirect product | (C2×C5)⋊(Q8×C9) |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C5 ⋊ C2×Q8×C9 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | #13083748, #13083749, #13083750, … |
| maximal normal subgroup of | #13083748, #13083749, #13083750, … |
| maximal quotient of | C4×C9×Dic10, C9×#4015, C9×#4016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 155);