Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #67180 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#67184 |
| Fitting | C23×C32×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×D4 |
| Sylow | C32 ⋊ C2×C22⋊D5 |
| Sylow | C5 ⋊ C2×#638 |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
186 conjugacy classes — view the full character table.
| maximal subgroup of | #13084765, #13084873, #13085089, … |
| maximal normal subgroup of | #13084765, #13084873, #13085089, … |
| maximal quotient of | C2×#10623906, #13088193, C2×#10623908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 758);