Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ #102 |
108 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 30 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:
2^5,5^2|a^2=c,c^2=e,d^2=e,b^a=bd,g^a=g^2,c^b=ce,d^b=de,f^b=f^4,g^c=g^459 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#677, AGL(1,𝔽5)×D40, #13103441, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#677, AGL(1,𝔽5)×D40, #13103441, … |
| maximal quotient of | #13099719, #13099721, #13099724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 394);