Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#1035)⋊C4 |
| Fitting | C2×C4×C25 ⋊ C4 |
| Sylow | C25 ⋊ #95 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,f^5=g,b^a=be,f^a=f^2g,g^a=g^2,f^c=f^4g^4,g^c=g^468 conjugacy classes — view the full character table.
| maximal subgroup of | #13097858, #13097859, #13097911, … |
| maximal normal subgroup of | #13097858, #13097859, #13097911, … |
| maximal quotient of | #13097848, #13097849, #13097852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 81);