Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D5×#135 |
| Fitting | C2×C5×#135 ⋊ C2 |
| Sylow | C5 ⋊ C22×#135 |
1504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #12014953, #12014957, D5×#1876, … |
| maximal normal subgroup of | #12014953, #12014957, D5×#1876, … |
| maximal quotient of | C2×D5×#416, C2×D5×#427, C2×C4×D5×D8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21165);