Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #6045⋊C5 |
| Sylow | H(3,𝔽5) ⋊ Q8 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^2,5,2,5^2|a^2=d,b^2=d,b^a=bd,e^a=e^4,f^a=f^4,e^c=ef73 conjugacy classes — view the full character table.
| maximal subgroup of | #14522130, #14522132, #14522136, … |
| maximal normal subgroup of | #14522130, #14522132, #14522136, … |
| maximal quotient of | #87806⋊C5, C4⋊(#1039⋊C5), C2×#6045⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 53);