Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #2923 |
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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|a^2=f,c^2=e,f^2=g,b^a=be,c^a=cg,h^a=h^4,d^b=dg,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11996124, #11996128, #11996131, … |
| maximal normal subgroup of | #11996124, #11996128, #11996131, … |
| maximal quotient of | #12096792, #12096838, #12097198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12333);