Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#525 ⋊ C2 |
| Sylow | C5 ⋊ #3003 |
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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,e^b=eg,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11997324, #11997326, #12071695, … |
| maximal normal subgroup of | #11997324, #11997326, #12071695, … |
| maximal quotient of | #12071669, #12071708, #12071747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16740);