Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
No aliases for this group.
| Fitting | C2×C52×#41 ⋊ C2 |
| Sylow | C52 ⋊ #575 |
1048 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|c^2=f,e^2=f,d^a=de,e^a=ef,g^a=g^4,h^a=h^4,d^b=df,e^d=ef262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9705);