Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C53 |
| unambiguous semidirect product | C22⋊#92553 |
| Sylow | C53 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×C5⋊(C5⋊D5) |
| commutator | C2×C53 | C2×C4 |
| Fitting, prime radical | C23×C53 | C2 |
| socle, cosocle | C22×C53 | C22 |
| hypercenter | C23 | C5⋊(C5⋊D5) |
| hypocenter | C53 | C22⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C23 | |
1088 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1000 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^a=bc,e^a=e^4,f^a=f^4,g^a=g^4506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 616);