Finite Group DatabasebetaFinite Group Databasebeta| order | 1444 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic19 |
| unambiguous semidirect product | C19⋊(C4×C19) |
| derived | C19 ⋊ C4×C19 |
| Sylow | C192 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D19 |
| commutator, hypocenter | C19 | C4×C19 |
| Frattini | C2 | C19×D19 |
| Fitting, socle, prime radical | C2×C192 | C2 |
| cosocle | C2×C19 | C2×C19 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C19 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 76 |
418 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×(C19⋊C3)⋊C4, #16864560, #16864561, … |
| maximal normal subgroup of | C19×(C19⋊C3)⋊C4, #16864560, #16864561, … |
| maximal quotient of | C3×C19×Dic19, C19×Dic57, C19×C19⋊#157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1444, 5);