Finite Group DatabasebetaFinite Group Databasebeta| order | 550 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D11⋊C25 |
| unambiguous semidirect product | (C11⋊C25)⋊C2 |
| derived, Sylow | C11 ⋊ C2×C25 |
| Hall | C11⋊C25 ⋊ C2 |
| Hall | D11 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C2×C25 |
| Fitting, socle, cosocle | C5×C11 | C2×C5 |
| prime radical | C5×D11 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 275 |
Polycyclic presentation:
2,5^2,11|b^5=c,d^a=d^10,d^b=d^955 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D11⋊C25, C3×D11⋊C25, C3⋊(D11⋊C25), … |
| maximal normal subgroup of | C2×D11⋊C25, C3×D11⋊C25, C7×D11⋊C25, … |
| maximal quotient of | Dic11⋊C25, C2×D11⋊C25, C3×D11⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(550, 1);