Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D5×#367 |
| Fitting | C5×#367 ⋊ C2 |
| Sylow | C5 ⋊ C2×#367 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1418, D5×#1426, C2×D5×#367, … |
| maximal normal subgroup of | D5×#1418, D5×#1426, C2×D5×#367, … |
| maximal quotient of | D5×#1372, #12010943, #12010983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2219);