Finite Group DatabasebetaFinite Group Databasebeta| order | 19476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#19096459⋊C2 |
| unambiguous semidirect product | #19096459⋊C22 |
| unambiguous semidirect product | (C2×#19096459)⋊C2 |
| Fitting, socle | C2×C541 ⋊ C2×C9 |
| derived, Sylow | C541 ⋊ C22×C9 |
| Hall | #19096459 ⋊ C22 |
| Hall | C2×D541 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19096459⋊C2 |
| commutator, hypocenter | C541 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C541 | C2×C9 |
| prime radical | C2×D541⋊C3 | C3 |
| cosocle | C541⋊C3 | C22×C3 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1082 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19476, 33);