Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Fitting | C52×M16 ⋊ C2 |
| Sylow | C52 ⋊ #104 |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^5,5^2|b^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^4,g^a=g^4,d^b=de134 conjugacy classes — view the full character table.
| maximal subgroup of | #13101169, #13101170, D5×#3957, … |
| maximal normal subgroup of | #13101169, #13101170, D5×#3957, … |
| maximal quotient of | #13099499, #13099500, #13099503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 351);