Finite Group DatabasebetaFinite Group Databasebeta| order | 26532 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C67⋊C9)⋊C11) |
| unambiguous semidirect product | (C67⋊C11)⋊(C22⋊C9) |
| unambiguous semidirect product | (C22⋊(C67⋊C9))⋊C11 |
| derived, Hall | C22×C67 ⋊ C9×C11 |
| Hall | C22×C67⋊C11 ⋊ C9 |
| Hall | C22⋊(C67⋊C9) ⋊ C11 |
| Hall | C67⋊C11 ⋊ C22⋊C9 |
| Sylow | C67 ⋊ C11×C22⋊C9 |
| Sylow | C22 ⋊ (C67⋊C9)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊((C67⋊C3)⋊C11) |
| commutator, hypocenter | C22×C67 | C9×C11 |
| Fitting, socle, cosocle | C22×C3×C67 | C3×C11 |
| prime radical | C22×C3×C67⋊C11 | C3 |
| LCS | G ▷ C22×C67 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1206 |
Polycyclic presentation:
3,11,2^2,67,3|a^3=f,c^a=d,d^a=cd,e^a=e^29,e^b=e^64156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26532, 23);