Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ C4 |
| Sylow | C5 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 124 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=e,b^2=f,c^2=e,e^2=g,b^a=bd,h^a=h^2,h^b=h^2,h^c=h^3,h^e=h^4,h^f=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #13016779, #13016783, #13016795, … |
| maximal normal subgroup of | #13016779, #13016783, #13016795, … |
| maximal quotient of | C22⋊C8×#170, #13016699, #13016706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 5995);