Finite Group DatabasebetaFinite Group Databasebeta| order | 550 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C5×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊C52 |
| unambiguous semidirect product | (C11⋊C5)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D11)⋊C5 |
| Fitting, socle | C5×C11 ⋊ C2×C5 |
| derived, Sylow | C11 ⋊ C2×C52 |
| Hall | C5×C11⋊C5 ⋊ C2 |
| Hall | D11 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 55 |
55 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(550, 7);