Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#376 ⋊ C2 |
| Sylow | C5 ⋊ #1963 |
320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 93 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=f,b^2=df,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^4,c^b=cg112 conjugacy classes — view the full character table.
| maximal subgroup of | #11986075, #11991652, #11991657, … |
| maximal normal subgroup of | #11986075, #11991652, #11991657, … |
| maximal quotient of | #11998086, #11998090, #11998094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2315);