Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 184 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) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,f^2=g,h^a=h^4,c^b=cg160 conjugacy classes — view the full character table.
| maximal subgroup of | #12010956, #12010960, #12014133, … |
| maximal normal subgroup of | #12010956, #12010960, #12014133, … |
| maximal quotient of | #12008282, #12008289, M16×#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2756);