Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D12×C31 |
| unambiguous semidirect product | C4⋊(D3×C31) |
| Fitting | C3×C4×C31 ⋊ C2 |
| Hall | C3×C31 ⋊ D4 |
| Sylow | C3 ⋊ D4×C31 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C31 | C2×D3 |
| commutator, cosocle | C2×C3 | C22×C31 |
| Frattini | C2 | C2×D3×C31 |
| Fitting | C3×C4×C31 | C2 |
| socle | C2×C3×C31 | C22 |
| hypercenter | C4×C31 | D3 |
| hypocenter | C3 | D4×C31 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C31 ◁ C4×C31 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 372 |
279 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13093433, #13093435, #13093437, … |
| maximal normal subgroup of | #13093433, #13093435, #13093437, … |
| maximal quotient of | C31×#204, C31×D24, C31×Dic12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 31);