Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic3×C31 |
| unambiguous semidirect product | (C2×C3)⋊(C4×C31) |
| derived, Sylow | C3 ⋊ C2×C4×C31 |
| Hall | C3×C31 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C31 | D3 |
| commutator, hypocenter | C3 | C2×C4×C31 |
| Frattini | C2 | C2×D3×C31 |
| Fitting, socle, prime radical | C22×C3×C31 | C2 |
| cosocle | C2×C3 | C22×C31 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C31 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 744 |
372 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×Dic31, (C2×D31)⋊Dic3, #13093448, … |
| maximal normal subgroup of | Dic3×Dic31, (C2×D31)⋊Dic3, #13093448, … |
| maximal quotient of | C2×C3⋊C8×C31, C31×#208, C4×Dic3×C31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 32);