Finite Group DatabasebetaFinite Group Databasebeta| order | 25205 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5041⋊C5 |
| Fitting, derived, Sylow | C5041 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5041 | C5 |
| Frattini, socle | C71 | C71⋊C5 |
| LCS | G ▷ C5041 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5041 |
Polycyclic presentation:
5,71^2|b^71=c,b^a=b^54c^38,c^a=c^541013 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25205, 1);