Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#65248 |
| Fitting | C22×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×#394 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12021090, C4×#65248, #12024605, … |
| maximal normal subgroup of | #12021090, C4×#65248, #12024605, … |
| maximal quotient of | C2×#10602343, C2×#10602340, C2×#10600221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15937);