Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | Q8×#676 |
| Fitting | C5×C8×Q8 ⋊ C2 |
| Sylow | C5 ⋊ Q8×M16 |
388 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #12070218, #12070224, #12070229, … |
| maximal normal subgroup of | #12070218, #12070224, #12070229, … |
| maximal quotient of | C4⋊C4×#676, #12097947, Q8×#3947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13732);