Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ #568 |
543 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 221 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=e,e^2=f,d^a=df,g^a=g^2,h^a=h^4,c^b=cf,g^e=g^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #72221502, #72221599, #72221600, … |
| maximal normal subgroup of | #72221502, #72221599, #72221600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10138);