Finite Group DatabasebetaFinite Group Databasebeta| order | 10406 |
| isoclinism | isoclinic class of C11⋊D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C11 |
| direct product | C43×C11⋊D11 |
| unambiguous semidirect product | C11⋊(D11×C43) |
| Fitting, socle, Hall | C112×C43 ⋊ C2 |
| derived, Sylow | C112 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | C11⋊D11 |
| commutator, cosocle, hypocenter | C112 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C112×C43 | C2 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C43 | |
56 conjugacy classes of subgroups.
2666 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#92150, C43⋊#92150, D112×C43, … |
| maximal normal subgroup of | C43×#92150, C43⋊#92150, D112×C43, … |
| maximal quotient of | C43×C11⋊Dic11, C2×C43×C11⋊D11, C3×C43×C11⋊D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10406, 7);