Finite Group DatabasebetaFinite Group Databasebeta| order | 34364 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×Dic71 |
| unambiguous semidirect product | C71⋊(C4×C121) |
| derived, Sylow | C71 ⋊ C4×C121 |
| Hall | C71×C121 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C121 | D71 |
| commutator, hypocenter | C71 | C4×C121 |
| Frattini | C2×C11 | C11×D71 |
| Fitting | C2×C71×C121 | C2 |
| socle, prime radical, cosocle | C2×C11×C71 | C2×C11 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C121 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34364 |
8954 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34364, 3);