Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#327 ⋊ C2 |
| Sylow | C5 ⋊ #1519 |
340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^c=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1519, C2×#10599100, #12066624, … |
| maximal normal subgroup of | D5×#1519, C2×#10599100, #12066624, … |
| maximal quotient of | #11987283, #11987287, #11987349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1182);