Finite Group DatabasebetaFinite Group Databasebeta| order | 26334 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#4296⋊D7) |
| unambiguous semidirect product | #4296⋊D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C11×C19 | C2×C9 |
| prime radical | C11⋊((C19⋊C3)⋊D7) | C3 |
| cosocle | C7×C11×C19⋊C3 | C2×C3 |
| LCS | G ▷ C7×C11×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1463 |
Polycyclic presentation:
2,3^2,7,11,19|b^3=c,d^a=d^6,e^a=e^10,f^a=f^18,f^b=f^4,f^c=f^7437 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26334, 76);