Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C3⋊AGL(1,𝔽23))⋊D11 |
| unambiguous semidirect product | (D33⋊D23)⋊C11 |
| unambiguous semidirect product | (C11⋊AGL(1,𝔽23))⋊D3 |
| Fitting, socle, derived | C3×C11×C23 ⋊ C22×C11 |
| Hall | C3×C11×C23⋊C11 ⋊ C22 |
| Hall | C11×C23⋊C11 ⋊ C2×D3 |
| Hall | C3×C23 ⋊ C2×C11×D11 |
| Sylow | C23 ⋊ D3×C11×D11 |
| Sylow | C3 ⋊ D11×AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C23 | C22×C11 |
| LCS | G ▷ C3×C11×C23 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
Polycyclic presentation:
2^2,11,3,11,23|e^a=e^10,f^a=f^22,d^b=d^2,e^b=e^10,f^c=f^2249 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 67);