Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C31 · Schur multiplier (H2) = C1 |
| direct product | C3⋊C8×C31 |
| unambiguous semidirect product | C3⋊(C8×C31) |
| derived, Sylow | C3 ⋊ C8×C31 |
| Hall | C3×C31 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C31 | D3 |
| commutator, hypocenter | C3 | C8×C31 |
| Frattini | C4 | D3×C31 |
| Fitting | C3×C4×C31 | C2 |
| socle, prime radical | C2×C3×C31 | C4 |
| cosocle | C3×C4 | C2×C31 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 744 |
372 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊C8×D31, D93⋊C8, #13093430, … |
| maximal normal subgroup of | C3⋊C8×D31, D93⋊C8, #13093430, … |
| maximal quotient of | C31×C3⋊C16, C2×C3⋊C8×C31 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 3);