Finite Group DatabasebetaFinite Group Databasebeta| order | 1922 |
| isoclinism | isoclinic class of C31⋊D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C31 |
| unambiguous semidirect product | C31⋊D31 |
| Fitting, socle, derived, Sylow | C312 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C312 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 961 |
Polycyclic presentation:
2,31^2|b^a=b^30,c^a=c^30482 conjugacy classes — view the full character table.
| maximal subgroup of | D312, #16838652, C2×C31⋊D31, … |
| maximal normal subgroup of | D312, #16838652, C2×C31⋊D31, … |
| maximal quotient of | C31⋊Dic31, C2×C31⋊D31, C7⋊(C31⋊D31), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1922, 4);