Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5 ⋊ #1373 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^4172 conjugacy classes — view the full character table.
| maximal subgroup of | #11986762, #11986763, #11986765, … |
| maximal normal subgroup of | #11986762, #11986763, #11986765, … |
| maximal quotient of | #11986040, #11986042, #11986184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 75);