Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ #360 |
120 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 19 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=df,d^2=e,e^2=f,b^a=bcdef,d^a=de,e^a=ef,g^a=g^2,h^a=h^3,c^b=cf,g^b=h^4,h^b=g^4,g^c=g^4,h^c=h^470 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2303);