Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C52 ⋊ #489 |
268 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|b^2=f,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^4,c^b=cdef,d^b=df,h^b=h^4,d^c=df112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 3033);