Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ #108 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bd,g^a=g^4,d^b=de,f^b=f^498 conjugacy classes — view the full character table.
| maximal subgroup of | #13100570, #13100571, D5×#3951, … |
| maximal normal subgroup of | #13100570, #13100571, D5×#3951, … |
| maximal quotient of | #13099267, #13099269, #13099335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 277);