Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C22×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ #3058 |
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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|b^2=eg,e^2=g,b^a=be,c^a=cf,e^a=eg,d^c=dg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12016746, #12016771, #12018030, … |
| maximal normal subgroup of | #12016746, #12016771, #12018030, … |
| maximal quotient of | #12082367, #12082406, #12082454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17649);