Finite Group DatabasebetaFinite Group Databasebeta| order | 1444 |
| isoclinism | isoclinic class of C19⋊D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C19⋊Dic19 |
| derived, Sylow | C192 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊D19 |
| commutator, hypocenter | C192 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C192 | C2 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1444 |
Polycyclic presentation:
2^2,19^2|a^2=b,c^a=c^18,d^a=d^18364 conjugacy classes — view the full character table.
| maximal subgroup of | #16864558, #16864559, (C19⋊C3)⋊Dic19, … |
| maximal normal subgroup of | #16864558, #16864559, (C19⋊C3)⋊Dic19, … |
| maximal quotient of | C3×C19⋊Dic19, C3⋊(C19⋊Dic19), C19⋊(C19⋊#157), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1444, 6);