Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×#117 ⋊ C2 |
| Sylow | C5 ⋊ #2395 |
560 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 560 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) = 320 |
Polycyclic presentation:
2^7,5|b^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^c=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11994276, #11994281, #12071453, … |
| maximal normal subgroup of | #11994276, #11994281, #12071453, … |
| maximal quotient of | #12020976, #12020995, #12021010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16087);