Finite Group DatabasebetaFinite Group Databasebeta| order | 560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×Q8×D7 |
| Fitting | C5×C7×Q8 ⋊ C2 |
| Hall | C5×C7 ⋊ C2×Q8 |
| Sylow | C7 ⋊ C2×C5×Q8 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#688, D7×#689, #11764961, … |
| maximal normal subgroup of | D7×#688, D7×#689, #11764961, … |
| maximal quotient of | C5×#6450, C5×#6459, C5×#6452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(560, 142);