Finite Group DatabasebetaFinite Group Databasebeta| order | 21550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D431⋊C25 |
| unambiguous semidirect product | (C431⋊C25)⋊C2 |
| derived, Sylow | C431 ⋊ C2×C25 |
| Hall | C431⋊C25 ⋊ C2 |
| Hall | D431 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D431⋊C5 |
| commutator, hypocenter | C431 | C2×C25 |
| Fitting, socle, cosocle | C5×C431 | C2×C5 |
| prime radical | C5×D431 | C5 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10775 |
Polycyclic presentation:
2,5,431,5|b^5=d,c^a=c^430,c^b=c^95265 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21550, 2);