Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C5×#335 ⋊ C2 |
| Sylow | C5 ⋊ #1572 |
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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=e,b^2=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,h^b=h^4,h^c=h^494 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1572, C2×#10599366, #12068370, … |
| maximal normal subgroup of | D5×#1572, C2×#10599366, #12068370, … |
| maximal quotient of | #11988778, #11990506, #11990514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1448);