Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of D3×D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic3×D31 |
| unambiguous semidirect product | (C3×D31)⋊C4 |
| derived, Hall | C3×C31 ⋊ C2×C4 |
| Sylow | C31 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C4×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D31 |
| commutator, hypocenter | C3×C31 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C31 | C22 |
| prime radical | C2×C3×D31 | C2 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 372 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | Dic6×D31, #13093541, #13093542, … |
| maximal normal subgroup of | Dic6×D31, #13093541, #13093542, … |
| maximal quotient of | C3⋊C8×D31, #13093430, Dic3×Dic31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 12);