Finite Group DatabasebetaFinite Group Databasebeta| order | 984 |
| isoclinism | isoclinic class of D3×D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×D41 |
| derived, Hall | C3×C41 ⋊ C2×C4 |
| Sylow | C41 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C4×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D41 |
| commutator, hypocenter | C3×C41 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C41 | C22 |
| prime radical | C2×C3×D41 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 492 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#4223, Dic3⋊#4223, Dic6×D41, … |
| maximal normal subgroup of | Dic3×#4223, Dic3⋊#4223, Dic6×D41, … |
| maximal quotient of | C3⋊C8×D41, #14520087, Dic3×Dic41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(984, 7);