Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×C4⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ #3239 |
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=eg,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^4,c^b=ceg,f^c=fg82 conjugacy classes — view the full character table.
| maximal subgroup of | #11996304, #11996310, #11996570, … |
| maximal normal subgroup of | #11996304, #11996310, #11996570, … |
| maximal quotient of | #12108835, #12109040, #12109864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17031);