Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Sylow | C52 ⋊ C2×M16 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=e,d^2=e,c^a=ce,f^a=f^3,g^a=g^2,f^d=f^4,g^d=g^468 conjugacy classes — view the full character table.
| maximal subgroup of | #13099896, #13099899, #13099905, … |
| maximal normal subgroup of | #13099896, #13099899, #13099905, … |
| maximal quotient of | #13104814, C4×#87863, #13104816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1107);