Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #356 |
132 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 17 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=c,b^2=de,c^2=f,d^2=f,b^a=bcdf,d^a=def,e^a=ef,g^a=g^2,h^a=h^3,c^b=ce,d^b=df,e^b=ef,g^b=h^4,h^b=g^4,d^c=df,g^c=g^4,h^c=h^461 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2344);