Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #416 |
358 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 63 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=d,b^2=f,c^2=f,d^2=f,e^2=f,c^a=ce,g^a=g^2,h^a=h^2,g^b=g^4,d^c=df,e^c=ef,g^d=g^4,h^d=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #72220873, #72220884, #72220886, … |
| maximal normal subgroup of | #72220873, #72220884, #72220886, … |
| maximal quotient of | #72242505, #72253308 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6433);