Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ #2148 |
220 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=g,d^2=f,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^4,d^b=dfg,e^b=eg,f^b=fg,h^b=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #12014564, #12014565, #12014599, … |
| maximal normal subgroup of | #12014564, #12014565, #12014599, … |
| maximal quotient of | #12009067, #12009072, #12009303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4317);