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 |
152 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 46 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|b^2=c,c^2=e,d^2=ef,e^2=f,b^a=bd,c^a=ce,d^a=de,e^a=ef,h^a=h^4,d^b=df,g^b=g^4148 conjugacy classes — view the full character table.
| maximal subgroup of | #72220701, #72220753, #72220754, … |
| maximal normal subgroup of | #72220701, #72220753, #72220754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1646);