Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #413 |
464 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 72 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=e,b^2=e,c^2=f,e^2=f,c^a=cd,d^a=df,g^a=g^4,c^b=cdf,d^b=df,h^b=h^4,e^c=ef106 conjugacy classes — view the full character table.
| maximal subgroup of | #72221116, #72223154, #72223168, … |
| maximal normal subgroup of | #72221116, #72223154, #72223168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4161);