Finite Group DatabasebetaFinite Group Databasebeta| order | 11322 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C37 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D3×C37 |
| unambiguous semidirect product | C3⋊(D3×C17×C37) |
| Fitting, socle, Hall | C32×C17×C37 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C17×C37 |
| Hall | C32×C37 ⋊ C2×C17 |
| Hall | C32×C17 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C37 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C17×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C37 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C17×C37 | |
48 conjugacy classes of subgroups.
3774 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×#157×C37, C17×#13050653, C37×#10597480, … |
| maximal normal subgroup of | C17×#157×C37, C17×#13050653, C37×#10597480, … |
| maximal quotient of | C17×C3⋊Dic3×C37, C2×C17×C3⋊D3×C37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11322, 29);