Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C52×Q8 ⋊ C2×C4 |
| Sylow | C52 ⋊ #417 |
366 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 366 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,c^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^2,h^a=h^2,c^b=cf,g^b=g^4,e^c=ef,g^d=g^4,h^d=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | #72220860, #72220864, #72220896, … |
| maximal normal subgroup of | #72220860, #72220864, #72220896, … |
| maximal quotient of | #72242572, #72253301 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6423);