Finite Group DatabasebetaFinite Group Databasebeta| order | 1968 |
| isoclinism | isoclinic class of #66502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#66502 |
| Fitting, socle | C2×C3×C41 ⋊ C8 |
| derived, Sylow | C41 ⋊ C2×C3×C8 |
| Hall | C3×C41 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #66502 |
| commutator, hypocenter | C41 | C2×C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C41 | C8 |
| prime radical | C2×C3×D41 | C4 |
| cosocle | #4223 | C22×C3 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 246 |
78 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#66502, C2×C3×AGL(1,𝔽41), C3×D3×#66502 |
| maximal normal subgroup of | C2×D3×#66502, C2×C3×AGL(1,𝔽41) |
| maximal quotient of | C3×D3×#66502 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1968, 189);