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 |
138 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 23 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|a^2=c,b^a=bd,d^a=de,f^a=f^3,g^a=g^3,c^b=ce,f^b=f^4,f^c=f^4,g^c=g^435 conjugacy classes — view the full character table.
| maximal subgroup of | #13103924, #13103925, D5⋊#3999, … |
| maximal normal subgroup of | #13103924, #13103925, D5⋊#3999, … |
| maximal quotient of | #13099882, #13099883, #13099884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 439);