Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊(C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | C3⋊(C11×C3⋊AGL(1,𝔽11)) |
| unambiguous semidirect product | (C11⋊C5)⋊(C11×C3⋊D3) |
| unambiguous semidirect product | (C3⋊D33)⋊(C5×C11) |
| Fitting, socle, Hall | C32×C112 ⋊ C2×C5 |
| derived | C32×C11 ⋊ C2×C5×C11 |
| Hall | C32×C11×C11⋊C5 ⋊ C2 |
| Hall | C11×C3⋊D33 ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ C11×AGL(1,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C3⋊AGL(1,𝔽11)) |
| commutator, cosocle, hypocenter | C32×C11 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C2×C5 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C11 | |
102 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 115);