Finite Group DatabasebetaFinite Group Databasebeta| order | 1922 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D31 |
| unambiguous semidirect product | C31⋊(C2×C31) |
| Fitting, socle, Sylow | C312 ⋊ C2 |
| derived | C31 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D31 |
| commutator, cosocle, hypocenter | C31 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C312 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C31 | |
23 conjugacy classes of subgroups.
| transitive degree | μt(G) = 62 |
527 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D312, C2×C31×D31, C31×D217, … |
| maximal normal subgroup of | D312, C2×C31×D31, C7×C31×D31, … |
| maximal quotient of | C31×Dic31, C2×C31×D31, C31×D217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1922, 3);