Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#3955 |
| Fitting | C4×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #11989857, C8×#3955, #11989867, … |
| maximal normal subgroup of | #11989857, C8×#3955, #11989867, … |
| maximal quotient of | C4×#64688, #11989811, #11989824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2744);