Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C52×C8 ⋊ C4 |
| Sylow | C52 ⋊ #107 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^4,g^a=g^3,g^c=g^486 conjugacy classes — view the full character table.
| maximal subgroup of | #13099719, #13099721, #13099738, … |
| maximal normal subgroup of | #13099719, #13099721, #13099738, … |
| maximal quotient of | #13100133, #13100134, #13100135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 496);