Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C16×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C3⋊C16 |
| unambiguous semidirect product | C3⋊(C16×C19) |
| derived, Sylow | C3 ⋊ C16×C19 |
| Hall | C3×C19 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C19 | D3 |
| commutator, hypocenter | C3 | C16×C19 |
| Frattini | C8 | D3×C19 |
| Fitting | C3×C8×C19 | C2 |
| socle, prime radical | C2×C3×C19 | C8 |
| cosocle | C3×C8 | C2×C19 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C8×C19 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 912 |
456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×C3⋊C16, D57⋊C16, #14268824, … |
| maximal normal subgroup of | D19×C3⋊C16, D57⋊C16, #14268824, … |
| maximal quotient of | C19×C3⋊C32, C2×C19×C3⋊C16 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 3);