Finite Group DatabasebetaFinite Group Databasebeta| order | 33396 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C121 · Schur multiplier (H2) = C2 |
| derived, Hall | C22×C23 ⋊ C3×C121 |
| Hall | C22×C23⋊C121 ⋊ C3 |
| Hall | A4×C23 ⋊ C121 |
| Sylow | C23 ⋊ A4×C121 |
| Sylow | C22 ⋊ C3×C23⋊C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C11 | A4×C23⋊C11 |
| commutator, hypocenter | C22×C23 | C3×C121 |
| Fitting, socle, cosocle | C22×C11×C23 | C3×C11 |
| prime radical | C11×A4×C23 | C11 |
| LCS | G ▷ C22×C23 | |
| UCS | C1 ◁ C11 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11132 |
572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33396, 15);