Finite Group DatabasebetaFinite Group Databasebeta| order | 11322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D333 |
| unambiguous semidirect product | C9⋊(C17×D37) |
| unambiguous semidirect product | C37⋊(C17×D9) |
| Fitting, Hall | C9×C17×C37 ⋊ C2 |
| derived, Hall | C9×C37 ⋊ C2×C17 |
| Hall | C17×C37 ⋊ D9 |
| Hall | C9×C17 ⋊ D37 |
| Sylow | C37 ⋊ C17×D9 |
| Sylow | C9 ⋊ C17×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D333 |
| commutator, cosocle, hypocenter | C9×C37 | C2×C17 |
| Frattini | C3 | C17×D111 |
| Fitting | C9×C17×C37 | C2 |
| socle | C3×C17×C37 | D3 |
| LCS | G ▷ C9×C37 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
2856 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D9×D37, D17×D333, D153⋊D37, … |
| maximal normal subgroup of | C17×D9×D37, D17×D333, D153⋊D37, … |
| maximal quotient of | C17×Dic333, C2×C17×D333 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11322, 7);