Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×H(5,𝔽2) ⋊ C2 |
| Sylow | C5 ⋊ #3019 |
762 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^4,e^b=eg,f^b=fg,e^c=eg97 conjugacy classes — view the full character table.
| maximal subgroup of | #12130590, #12130594, #12130601, … |
| maximal normal subgroup of | #12130590, #12130594, #12130601, … |
| maximal quotient of | #12071670, #12071677, #12071709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17917);