Finite Group DatabasebetaFinite Group Databasebeta| order | 744 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| direct product | C8×C31⋊C3 |
| unambiguous semidirect product | (C8×C31)⋊C3 |
| Fitting, Hall | C8×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C8 |
| Frattini | C4 | C2×C31⋊C3 |
| Fitting | C8×C31 | C3 |
| socle | C2×C31 | C3×C4 |
| prime radical | C2×C31⋊C3 | C4 |
| cosocle | C4×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C8 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 248 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | (C31⋊C3)⋊C16, C16×C31⋊C3, C8×D31⋊C3, … |
| maximal normal subgroup of | (C31⋊C3)⋊C16, C16×C31⋊C3, C8×D31⋊C3, … |
| maximal quotient of | C16×C31⋊C3, C2×C8×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(744, 2);