Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C25 ⋊ C4 |
| Sylow | C25 ⋊ #342 |
213 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,g^5=h,b^a=be,d^a=df,g^a=g^2h,h^a=h^2,e^b=ef,g^c=g^4h^4,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#1035, #72275692, #72275694, … |
| maximal normal subgroup of | #99×#1035, #72275692, #72275694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 205);