Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C19 · Schur multiplier (H2) = C2×C7 |
| direct product | C19×C22⋊#89205 |
| unambiguous semidirect product | C22⋊(C19×#89205) |
| derived, Hall | C22×C72 ⋊ C9×C19 |
| Hall | C22×C72×C19 ⋊ C9 |
| Hall | C72×C19 ⋊ C22⋊C9 |
| Hall | C22×C19 ⋊ #89205 |
| Sylow | C72 ⋊ C19×C22⋊C9 |
| Sylow | C22 ⋊ C19×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | C22⋊#3862 |
| commutator, hypocenter | C22×C72 | C9×C19 |
| Frattini | C3 | C19×C22⋊#3862 |
| Fitting, socle, prime radical | C22×C3×C72×C19 | C3 |
| cosocle | C22×C3×C72 | C3×C19 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C3×C19 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2394 |
3876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 487);