Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×D20 |
| Fitting | C4×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | #12088656, #12088664, #12088671, … |
| maximal normal subgroup of | #12088656, #12088664, #12088671, … |
| maximal quotient of | #12088772, #12088787, #12088802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13486);