Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C52×M16 ⋊ C22 |
| Sylow | C52 ⋊ C2×AGL(1,ℤ/8) |
664 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 130 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|d^2=e,e^2=f,d^a=de,e^a=ef,g^a=g^4,d^b=de,e^b=ef,h^b=h^4,d^c=df106 conjugacy classes — view the full character table.
| maximal subgroup of | D52×AGL(1,ℤ/8), #72220868, #72220915, … |
| maximal normal subgroup of | D52×AGL(1,ℤ/8), #72220868, #72220915, … |
| maximal quotient of | #72242537 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8159);