Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×Q8×D9 |
| Fitting | C5×Q8×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ C2×C5×Q8 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#688, #13084273, D9×#689, … |
| maximal normal subgroup of | D9×#688, #13084273, D9×#689, … |
| maximal quotient of | C5×#63449, C5×#63458, C5×#63450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 171);