Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D17×C13⋊C3 |
| unambiguous semidirect product | C17⋊(C22×C13×C13⋊C3) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C13×C13⋊C3) |
| unambiguous semidirect product | (C2×C13×D17)⋊(C3×C13) |
| Fitting, socle | C2×C132×C17 ⋊ C2×C3 |
| derived | C13×C17 ⋊ C22×C3×C13 |
| Hall | C2×C132×D17 ⋊ C3 |
| Hall | C13×C17×C13⋊C3 ⋊ C22 |
| Hall | C132×C17 ⋊ C22×C3 |
| Sylow | C132 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C22×C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D17×C13⋊C3 |
| commutator, cosocle, hypocenter | C13×C17 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C17 | C2×C3 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C2×C13 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1326 |
1820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 179);