Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×#711 |
| Fitting | C5×C8×D4 ⋊ C2 |
| Sylow | C5 ⋊ C8×#41 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12009129, #12009139, #12009169, … |
| maximal normal subgroup of | #12009129, #12009139, #12009169, … |
| maximal quotient of | C8×#4023, C8×#4038, C8×#4027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13212);