Finite Group DatabasebetaFinite Group Databasebeta| order | 34362 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊D249 |
| unambiguous semidirect product | C3⋊(C23×D249) |
| unambiguous semidirect product | C83⋊(C3⋊D3×C23) |
| Fitting, socle, Hall | C32×C23×C83 ⋊ C2 |
| derived, Hall | C32×C83 ⋊ C2×C23 |
| Hall | C23×C83 ⋊ C3⋊D3 |
| Hall | C32×C23 ⋊ D83 |
| Sylow | C83 ⋊ C3⋊D3×C23 |
| Sylow | C32 ⋊ C23×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊D249 |
| commutator, cosocle, hypocenter | C32×C83 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C23×C83 | C2 |
| LCS | G ▷ C32×C83 | |
| UCS | C1 ◁ C23 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17181 |
8625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34362, 18);