Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2368 |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=f,c^2=efg,b^a=be,c^a=cfg,h^a=h^4,d^b=de,h^b=h^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #11995864, #11995868, #11995878, … |
| maximal normal subgroup of | #11995864, #11995868, #11995878, … |
| maximal quotient of | #12020735, #12020811, #12020860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16562);