Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C25 ⋊ C2 |
| Sylow | C25 ⋊ #137 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=e,d^2=e,f^5=g,c^a=ce,f^a=f^4g^4,g^a=g^4,c^b=cd,d^b=de,d^c=de95 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11716480, #13099089, #13099091, … |
| maximal normal subgroup of | C2×#11716480, #13099089, #13099091, … |
| maximal quotient of | #13098063, #13098064, #13098068, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 139);