Finite Group DatabasebetaFinite Group Databasebeta| order | 738 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D41 |
| unambiguous semidirect product | C41⋊(C2×C32) |
| Fitting, socle, Hall | C32×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D41 |
| commutator, cosocle, hypocenter | C41 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 369 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#4223, C3×C3⋊#4223, C3⋊(C3⋊#4223), … |
| maximal normal subgroup of | C32×#4223, C3×C3⋊#4223, C3⋊(C3⋊#4223), … |
| maximal quotient of | C32×Dic41, C2×C32×D41, C32×C5×D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(738, 5);