Finite Group DatabasebetaFinite Group Databasebeta| order | 34518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D523⋊C3 |
| unambiguous semidirect product | D523⋊(C3×C11) |
| unambiguous semidirect product | (C523⋊C3)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D523)⋊C3 |
| Fitting, socle, Hall | C11×C523 ⋊ C2×C3 |
| derived, Sylow | C523 ⋊ C2×C3×C11 |
| Hall | C11×C523⋊C3 ⋊ C2 |
| Hall | C11×D523 ⋊ C3 |
| Hall | C523⋊C3 ⋊ C2×C11 |
| Hall | D523 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D523⋊C3 |
| commutator, cosocle, hypocenter | C523 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C523 | C2×C3 |
| LCS | G ▷ C523 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5753 |
1023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34518, 10);