Finite Group DatabasebetaFinite Group Databasebeta| order | 1992 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C3×C83⋊C8 |
| unambiguous semidirect product | C83⋊(C3×C8) |
| derived, Sylow | C83 ⋊ C3×C8 |
| Hall | C3×C83 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | D83 |
| commutator, hypocenter | C83 | C3×C8 |
| Frattini | C4 | C3×D83 |
| Fitting | C3×C4×C83 | C2 |
| socle, prime radical | C2×C3×C83 | C4 |
| cosocle | C4×C83 | C2×C3 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C3×C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 94 |
| transitive degree | μt(G) = 1992 |
516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1992, 2);