Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C13 |
| direct product | C17×#14523161 |
| Fitting, socle, Hall | C132×C17 ⋊ Dic3 |
| derived, Hall | #92789 ⋊ C4×C17 |
| Hall | C17×#92789 ⋊ C4 |
| Sylow | C132 ⋊ Dic3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #14523161 |
| commutator, hypocenter | #92789 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C132×C17 | Dic3 |
| prime radical | C17×#11759816 | C2 |
| cosocle | #11759816 | C2×C17 |
| LCS | G ▷ #92789 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 442 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 90);