Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C41 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊C8×C41 |
| unambiguous semidirect product | (C2×C3)⋊(C8×C41) |
| derived, Sylow | C3 ⋊ C2×C8×C41 |
| Hall | C3×C41 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C41 | D3 |
| commutator, hypocenter | C3 | C2×C8×C41 |
| Frattini | C4 | C2×D3×C41 |
| Fitting | C2×C3×C4×C41 | C2 |
| socle, prime radical | C22×C3×C41 | C4 |
| cosocle | C3×C4 | C22×C41 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C4×C41 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1968 |
984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3×C8×C41 |
| maximal normal subgroup of | C2×D3×C8×C41 |
| maximal quotient of | C2×C41×C3⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 54);