Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2275 |
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=g,c^2=f,b^a=be,d^a=de,h^a=h^4,c^b=ce,h^b=h^4,h^d=h^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #11996194, #11996198, #11996208, … |
| maximal normal subgroup of | #11996194, #11996198, #11996208, … |
| maximal quotient of | #12020381, #12020385, #12020578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7564);