Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×Dic5 |
| Sylow | C5 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12004728, #12004869, Dic5×#391, … |
| maximal normal subgroup of | #12004728, #12004869, Dic5×#391, … |
| maximal quotient of | C22×C4⋊C4×Dic5, C2×C4×Q8×Dic5, C22×#65270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21226);