Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ C2×Q16 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^4,c^b=cd,d^b=de,f^b=f^4,d^c=de62 conjugacy classes — view the full character table.
| maximal subgroup of | #13104077, #13104078, #13104079, … |
| maximal normal subgroup of | #13104077, #13104078, #13104079, … |
| maximal quotient of | #13100598, #13100628, #13100668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 721);