Finite Group DatabasebetaFinite Group Databasebeta| order | 11121 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C337⋊C3 |
| unambiguous semidirect product | C337⋊(C3×C11) |
| unambiguous semidirect product | (C11×C337)⋊C3 |
| Fitting, socle, Hall | C11×C337 ⋊ C3 |
| derived, Sylow | C337 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C337⋊C3 |
| commutator, cosocle, hypocenter | C337 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C337 | C3 |
| LCS | G ▷ C337 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
1265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C337⋊C3, C11×D337⋊C3, D11×C337⋊C3, … |
| maximal normal subgroup of | C2×C11×C337⋊C3, C11×D337⋊C3, D11×C337⋊C3, … |
| maximal quotient of | C2×C11×C337⋊C3, C11×C337⋊C9, C3×C11×C337⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11121, 1);