Finite Group DatabasebetaFinite Group Databasebeta| order | 1444 |
| isoclinism | isoclinic class of D192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D192 |
| unambiguous semidirect product | (C19×D19)⋊C2 |
| unambiguous semidirect product | (C19⋊D19)⋊C2 |
| Fitting, socle, derived, Sylow | C192 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C192 | C22 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 38 |
121 conjugacy classes — view the full character table.
| maximal subgroup of | #14524206⋊C2, #14524209⋊C2, D19×D19⋊C3, … |
| maximal normal subgroup of | #14524206⋊C2, #14524209⋊C2, D19×D19⋊C3, … |
| maximal quotient of | C3×D192, D19×D57, D57⋊D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1444, 9);