Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C25 ⋊ C2 |
| Sylow | C25 ⋊ C22⋊Q8 |
111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=e,f^5=g,c^a=cd,f^a=f^4g^4,g^a=g^4,c^b=ce134 conjugacy classes — view the full character table.
| maximal subgroup of | #13097917, #13098081, #13098083, … |
| maximal normal subgroup of | #13097917, #13098081, #13098083, … |
| maximal quotient of | #13098252, #13098253, #13098256, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 167);