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×#367 ⋊ C2 |
| Sylow | C5 ⋊ #2158 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=df,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^b=h^4,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12019761, #12019819, D5×#2158, … |
| maximal normal subgroup of | #12019761, #12019819, D5×#2158, … |
| maximal quotient of | #12010884, #12010948, #12010989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2220);