Finite Group DatabasebetaFinite Group Databasebeta| order | 11322 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C17×D37 |
| Fitting, socle, Hall | C32×C17×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C32×C17 |
| Hall | C17×C37 ⋊ C2×C32 |
| Hall | C32×C37 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C17 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C32×C17 | |
48 conjugacy classes of subgroups.
3060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C17×#3866, C32×#14578982, C32×D17×D37, … |
| maximal normal subgroup of | C32×C17×#3866, C32×#14578982, C32×D17×D37, … |
| maximal quotient of | C32×C17×Dic37, C2×C32×C17×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11322, 36);