Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #471 |
276 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 54 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|b^2=ef,c^2=f,e^2=f,b^a=be,c^a=ce,d^a=df,e^a=ef,g^a=g^4,c^b=cd,d^b=df,h^b=h^4,e^c=ef100 conjugacy classes — view the full character table.
| maximal subgroup of | #72221017, #72223049, #72223051, … |
| maximal normal subgroup of | #72221017, #72223049, #72223051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4177);