Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3165 |
380 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 380 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=e,b^2=e,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,d^c=dg112 conjugacy classes — view the full character table.
| maximal subgroup of | #11996809, #11996811, #11996846, … |
| maximal normal subgroup of | #11996809, #11996811, #11996846, … |
| maximal quotient of | #12099729, #12102690, #12103883, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12319);