Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C8×#704 |
| Sylow | C5 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013701, #13013702, #13013713, … |
| maximal normal subgroup of | #13013701, #13013702, #13013713, … |
| maximal quotient of | C8×#4002, #13015273, #13016665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6768);