Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| direct product | C3×C3⋊(C5⋊(C11⋊D11)) |
| unambiguous semidirect product | C3⋊(C3×C5⋊(C11⋊D11)) |
| unambiguous semidirect product | C5⋊(C3×C3⋊(C11⋊D11)) |
| unambiguous semidirect product | C11⋊(C3×D165) |
| Fitting, socle, Hall | C32×C5×C112 ⋊ C2 |
| derived | C3×C5×C112 ⋊ C2×C3 |
| Hall | C32×C112 ⋊ D5 |
| Hall | C5×C112 ⋊ C3×D3 |
| Sylow | C112 ⋊ C3×D15 |
| Hall | C32×C5 ⋊ C11⋊D11 |
| Sylow | C32 ⋊ C5⋊(C11⋊D11) |
| Sylow | C5 ⋊ C3×C3⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C5⋊(C11⋊D11)) |
| commutator, cosocle, hypocenter | C3×C5×C112 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C112 | C2 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 ◁ C3 | |
252 conjugacy classes of subgroups.
2727 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D11×D165, C3×D15×C11⋊D11, C3×D33×D55, … |
| maximal normal subgroup of | C3×D11×D165, C3×D15×C11⋊D11, C3×D33×D55, … |
| maximal quotient of | C3×C3⋊(C11⋊Dic55), C2×C3×C3⋊(C5⋊(C11⋊D11)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 152);