Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ #2943 |
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^4,e^b=eg,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #12014586, #12014588, #12015947, … |
| maximal normal subgroup of | #12014586, #12014588, #12015947, … |
| maximal quotient of | #12068708, #12068876, #12069079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12307);