Finite Group DatabasebetaFinite Group Databasebeta| order | 25055 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5011⋊C5 |
| Fitting, socle, derived, Sylow | C5011 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5011 | C5 |
| LCS | G ▷ C5011 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5011 |
Polycyclic presentation:
5,5011|b^a=b^2731007 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25055, 1);