Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2293 |
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,h^b=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #11989936, #11989946, #11989956, … |
| maximal normal subgroup of | #11989936, #11989946, #11989956, … |
| maximal quotient of | #12020409, #12020441, C4×#64958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7430);