Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C13 |
| direct product | C3×#26040095 |
| derived, Hall | C132×C17 ⋊ C3×C4 |
| Hall | C3×C132×C17 ⋊ C4 |
| Hall | C3×C132 ⋊ Dic17 |
| Sylow | C132 ⋊ C3×Dic17 |
| Hall | C3×C17 ⋊ #10621725 |
| Sylow | C17 ⋊ C3×#10621725 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C13⋊D221 |
| commutator, hypocenter | C132×C17 | C3×C4 |
| Frattini | C2 | C3×C13⋊D221 |
| Fitting, socle, prime radical | C2×C3×C132×C17 | C2 |
| cosocle | C2×C132×C17 | C2×C3 |
| LCS | G ▷ C132×C17 | |
| UCS | C1 ◁ C2×C3 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34476 |
8628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 82);