Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#10620310 |
| Fitting | C3×Q8×C41 ⋊ C2 |
| Hall | C3×C41 ⋊ #41 |
| Sylow | C41 ⋊ C3×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×D41 |
| commutator, cosocle | C2×C41 | C23×C3 |
| Frattini | C2 | C22×C3×D41 |
| Fitting | C3×Q8×C41 | C2 |
| socle | C2×C3×C41 | C23 |
| hypercenter | C3×Q8 | D41 |
| hypocenter | C41 | C3×#41 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2×C3 ◁ C3×Q8 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 984 |
330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 158);