Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#329 ⋊ C2 |
| Sylow | C5 ⋊ #1536 |
238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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,c^2=g,d^2=g,e^2=f,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^c=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #12019541, #12019557, D5×#1536, … |
| maximal normal subgroup of | #12019541, #12019557, D5×#1536, … |
| maximal quotient of | #11987395, #11987397, #11987419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1224);