Finite Group DatabasebetaFinite Group Databasebeta| order | 1476 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic123 |
| unambiguous semidirect product | C3⋊(C3×Dic41) |
| derived | C3×C41 ⋊ C3×C4 |
| Hall | C32×C41 ⋊ C4 |
| Sylow | C41 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D123 |
| commutator, hypocenter | C3×C41 | C3×C4 |
| Frattini | C2 | C3×D123 |
| Fitting, socle, prime radical | C2×C32×C41 | C2 |
| cosocle | C2×C3×C41 | C2×C3 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C3 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 492 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic123, C3×Dic1353, C3⋊(Dic533⋊C3), … |
| maximal normal subgroup of | C3×C11×Dic123, C3×C13×Dic123, C3×C17×Dic123, … |
| maximal quotient of | C3×C11×Dic123, C3×Dic1353, C3⋊(Dic533⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1476, 15);