Finite Group DatabasebetaFinite Group Databasebeta| order | 550 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D25 |
| unambiguous semidirect product | C25⋊(C2×C11) |
| Fitting, Hall | C11×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C11 |
| Frattini | C5 | D5×C11 |
| Fitting | C11×C25 | C2 |
| socle | C5×C11 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 275 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#1035, C11⋊#1035, D11×D25, … |
| maximal normal subgroup of | C11×#1035, C11⋊#1035, D11×D25, … |
| maximal quotient of | C11×Dic25, C2×C11×D25, C3×C11×D25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(550, 3);