Finite Group DatabasebetaFinite Group Databasebeta| order | 11322 |
| isoclinism | isoclinic class of #66526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×C17×#66526 |
| Fitting, socle, Hall | C2×C17×C37 ⋊ C9 |
| derived, Sylow | C37 ⋊ C2×C9×C17 |
| Hall | C17×C37 ⋊ C2×C9 |
| Hall | C2×C37 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | #66526 |
| commutator, hypocenter | C37 | C2×C9×C17 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C37 | C9 |
| prime radical | C2×C17×C37⋊C3 | C3 |
| cosocle | C37⋊C3 | C2×C3×C17 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C17 | |
24 conjugacy classes of subgroups.
442 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#13050625, #36383359, Dic17×#66526, … |
| maximal normal subgroup of | C17×#13050625, #36383359, Dic17×#66526, … |
| maximal quotient of | C4×C17×#66526, C22×C17×#66526 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11322, 17);