Finite Group DatabasebetaFinite Group Databasebeta| order | 23050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D461⋊C25 |
| unambiguous semidirect product | (C461⋊C25)⋊C2 |
| derived, Sylow | C461 ⋊ C2×C25 |
| Hall | C461⋊C25 ⋊ C2 |
| Hall | D461 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D461⋊C5 |
| commutator, hypocenter | C461 | C2×C25 |
| Fitting, socle, cosocle | C5×C461 | C2×C5 |
| prime radical | C5×D461 | C5 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11525 |
Polycyclic presentation:
2,5,461,5|b^5=d,c^a=c^460,c^b=c^88280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23050, 2);