Finite Group DatabasebetaFinite Group Databasebeta| order | 29766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊#10624391 |
| Fitting, socle, Hall | C112×C41 ⋊ D3 |
| derived, Hall | C41×C112⋊C3 ⋊ C2 |
| Hall | C112⋊C3 ⋊ D41 |
| Sylow | C112 ⋊ D123 |
| Sylow | C41 ⋊ #10624391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C41×C112⋊C3 | C2 |
| Fitting, socle | C112×C41 | D3 |
| LCS | G ▷ C41×C112⋊C3 | |
| UCS | C1 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1353 |
Polycyclic presentation:
2,3,41,11^2|b^a=b^2,c^a=c^40,d^a=de^4,e^a=e^10,d^b=d^2e^10,e^b=d^7e^8898 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29766, 12);