Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1776 |
272 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 272 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) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #12014591, #12014593, #12014720, … |
| maximal normal subgroup of | #12014591, #12014593, #12014720, … |
| maximal quotient of | #11990497, #11990502, #11990517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2689);