Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×C22⋊C4 |
318 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 66 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|c^2=d,c^a=ce,g^a=g^4,c^b=ce,f^b=f^492 conjugacy classes — view the full character table.
| maximal subgroup of | #13099959, #13103980, #13103989, … |
| maximal normal subgroup of | #13099959, #13103980, #13103989, … |
| maximal quotient of | #13100574, #13100575, #13100585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 698);