Finite Group DatabasebetaFinite Group Databasebeta| order | 1210 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×C11) |
| unambiguous semidirect product | (C11⋊C5)⋊(C2×C11) |
| Fitting, socle, Sylow | C112 ⋊ C2×C5 |
| derived | C11 ⋊ C2×C5×C11 |
| Hall | C11×C11⋊C5 ⋊ C2 |
| Hall | C11×D11 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11 | |
17 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 110 |
121 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1210, 8);