Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×D36 |
| Fitting | C2×C4×C5×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ C2×D4 |
| Sylow | C9 ⋊ C2×C5×D4 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | #13083717, #13083734, #13083738, … |
| maximal normal subgroup of | #13083717, #13083734, #13083738, … |
| maximal quotient of | C5×#63431, C4×C5×D36, C5×#63436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 167);