Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #465 |
342 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=e,b^2=ef,c^2=def,d^2=f,e^2=f,c^a=cef,g^a=g^4,c^b=cd,h^b=h^4,d^c=df,e^c=ef118 conjugacy classes — view the full character table.
| maximal subgroup of | #72242539, #72242551, #72242553 |
| maximal normal subgroup of | #72242539, #72242551, #72242553 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3088);