Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #341 |
248 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,c^2=f,d^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^3,h^a=h^2,e^b=ef,g^c=g^4,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #72221234, #72221236, #72221239, … |
| maximal normal subgroup of | #72221234, #72221236, #72221239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2724);