Finite Group DatabasebetaFinite Group Databasebeta| order | 24550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D491⋊C25 |
| unambiguous semidirect product | (C491⋊C25)⋊C2 |
| derived, Sylow | C491 ⋊ C2×C25 |
| Hall | C491⋊C25 ⋊ C2 |
| Hall | D491 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D491⋊C5 |
| commutator, hypocenter | C491 | C2×C25 |
| Fitting, socle, cosocle | C5×C491 | C2×C5 |
| prime radical | C5×D491 | C5 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12275 |
Polycyclic presentation:
2,5,491,5|b^5=d,c^a=c^490,c^b=c^381295 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24550, 2);