Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #99 |
113 conjugacy classes of subgroups; only the 15 normal subgroups are shown.
This group has 113 conjugacy classes of subgroups — too many to draw. Only its 15 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|b^2=d,b^a=bc,d^a=de,f^a=f^4,g^a=fg,c^b=ce,f^b=f^2g^4,g^b=f^3g^3,f^c=f^4,g^c=g^441 conjugacy classes — view the full character table.
| maximal subgroup of | #13104177, #13104178, #13104272, … |
| maximal normal subgroup of | #13104177, #13104178, #13104272, … |
| maximal quotient of | #13099959, #13099960, #13099965, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 455);