Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D81 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×C3⋊D81 |
| Fitting | C3×C4×C81 ⋊ C2 |
| derived, Sylow | C3×C81 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊D81 |
| commutator, hypocenter | C3×C81 | C2×C4 |
| Frattini | C2×C27 | C2×C3⋊D3 |
| Fitting | C3×C4×C81 | C2 |
| socle | C2×C32 | C2×D27 |
| prime radical | C2×C3⋊D81 | C2 |
| cosocle | C2×C3×C81 | C22 |
| LCS | G ▷ C3×C81 | |
| UCS | C1 ◁ C4 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 972 |
492 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 541);