Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #2308 |
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #12004686, #12004689, #12005628, … |
| maximal normal subgroup of | #12004686, #12004689, #12005628, … |
| maximal quotient of | #12020538, #12020543, #12020595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15934);