Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#4024 |
| Sylow | C5 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#4024, #12106711, #12106721, … |
| maximal normal subgroup of | C8×#4024, #12106711, #12106721, … |
| maximal quotient of | C4×#65239, C4×#65235, C4×#64944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7255);