Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| isoclinism | isoclinic class of D3×D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊C8 |
| derived, Hall | C3×C19 ⋊ C2×C8 |
| Sylow | C19 ⋊ D3×C8 |
| Sylow | C3 ⋊ C8×D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D19 |
| commutator, hypocenter | C3×C19 | C2×C8 |
| Fitting, cosocle | C3×C4×C19 | C22 |
| socle | C2×C3×C19 | C2×C4 |
| prime radical | C2×D57 | C4 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
Polycyclic presentation:
2^4,3,19|a^2=c,b^2=c,c^2=d,f^a=f^18,e^b=e^2132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C8×D19, #14269163, #14269183, … |
| maximal normal subgroup of | D3×C8×D19, #14269163, #14269183, … |
| maximal quotient of | D57⋊C16, #14268826, #14268841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 25);