Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C8×D4×D5 |
| Fitting | C5×C8×D4 ⋊ C2 |
| Sylow | C5 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D4⋊C16, #12009005, #12009209, … |
| maximal normal subgroup of | D5×D4⋊C16, #12009005, #12009209, … |
| maximal quotient of | C8×D5×D8, C8×D5×SD16, C8×D5×Q16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13233);