Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #2367 |
632 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^4,d^b=de,h^b=h^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #12121588, #12121590, #12121603, … |
| maximal normal subgroup of | #12121588, #12121590, #12121603, … |
| maximal quotient of | #12020748, #12020842, #12020869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16768);