Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#3941 |
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #11990063, C8×#3941, #11990077, … |
| maximal normal subgroup of | #11990063, C8×#3941, #11990077, … |
| maximal quotient of | C4×#64703, #11989925, #11989940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2347);