Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 137 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=d,b^2=e,d^2=f,e^2=g,c^a=cf,h^a=h^4,h^b=h^4160 conjugacy classes — view the full character table.
| maximal subgroup of | #11989857, #11989861, #11989862, … |
| maximal normal subgroup of | #11989857, #11989861, #11989862, … |
| maximal quotient of | #11988654, #11988683, #11989727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3614);