Finite Group DatabasebetaFinite Group Databasebeta| order | 19228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C19⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C2×C19)⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C2×C23⋊C11)⋊D19 |
| unambiguous semidirect product | (C2×D437)⋊C11 |
| Fitting, socle | C2×C19×C23 ⋊ C2×C11 |
| derived, Hall | C19×C23 ⋊ C22×C11 |
| Hall | C19×C23⋊C11 ⋊ C22 |
| Hall | C2×D437 ⋊ C11 |
| Hall | C23⋊C11 ⋊ C2×D19 |
| Sylow | C23 ⋊ C2×C11×D19 |
| Sylow | C19 ⋊ C2×AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C19×C23 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C23 | C2×C11 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 874 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19228, 16);