Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#4042 |
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| 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×#4042, #12106713, #12106723, … |
| maximal normal subgroup of | C8×#4042, #12106713, #12106723, … |
| maximal quotient of | C4×#65278, C4×#64957, C4×#65270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7572);