Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C52 ⋊ #386 |
808 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=f,b^2=ef,b^a=be,g^a=g^4,c^b=cd,h^b=h^4196 conjugacy classes — view the full character table.
| maximal subgroup of | #72223321 |
| maximal normal subgroup of | #72223321 |
| maximal quotient of | #72223317, #72223328, #72223332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4238);