Finite Group DatabasebetaFinite Group Databasebeta| order | 29868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D131 |
| unambiguous semidirect product | D393⋊D19 |
| unambiguous semidirect product | D2489⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C131 ⋊ C22 |
| Hall | C19×C131 ⋊ C2×D3 |
| Hall | C3×C131 ⋊ C2×D19 |
| Sylow | C131 ⋊ D3×D19 |
| Hall | C3×C19 ⋊ C2×D131 |
| Sylow | C19 ⋊ D3×D131 |
| Sylow | C3 ⋊ D19×D131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C131 | C22 |
| LCS | G ▷ C3×C19×C131 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7467 |
Polycyclic presentation:
2^2,3,19,131|d^a=d^18,e^a=e^130,c^b=c^2,d^b=d^181983 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29868, 24);