Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2103 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #12012659, #12012661, #12012664, … |
| maximal normal subgroup of | #12012659, #12012661, #12012664, … |
| maximal quotient of | #12004425, #12004430, #12004435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3414);