Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D4 |
242 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20 |
Polycyclic presentation:
2^5,5^2|a^2=d,f^a=f^3,g^a=g^3,c^b=ce,f^b=f^4,f^d=f^4,g^d=g^438 conjugacy classes — view the full character table.
| maximal subgroup of | #13107479, #13107501, #13107509, … |
| maximal normal subgroup of | #13107479, #13107501, #13107509, … |
| maximal quotient of | #13103974, #13103977, #13103989, … |
| holomorph of | Dic5, C2×D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1034);