Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×C22⋊#92788 |
| unambiguous semidirect product | C22⋊(C17×#92788) |
| unambiguous semidirect product | (C22×C17)⋊#92788 |
| Fitting, socle, Hall | C22×C132×C17 ⋊ C3 |
| derived, Hall | C22×C132 ⋊ C3×C17 |
| Hall | C132×C17 ⋊ A4 |
| Sylow | C132 ⋊ A4×C17 |
| Hall | C22×C17 ⋊ #92788 |
| Sylow | C22 ⋊ C17×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C22⋊#92788 |
| commutator, cosocle, hypocenter | C22×C132 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C22×C132×C17 | C3 |
| LCS | G ▷ C22×C132 | |
| UCS | C1 ◁ C17 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11492 |
3876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 257);