Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#22552710 |
| derived, Hall | C72×C19 ⋊ C22×C9 |
| Hall | C22×C72×C19 ⋊ C9 |
| Hall | C22×C72 ⋊ #4294 |
| Hall | C22×C19 ⋊ #89204 |
| Sylow | C72 ⋊ C22×#4294 |
| Sylow | C19 ⋊ C22×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #14584116 |
| commutator, hypocenter | C72×C19 | C22×C9 |
| Frattini | C3 | C22×#14584116 |
| Fitting, socle, prime radical | C22×C3×C72×C19 | C3 |
| cosocle | C3×C72×C19 | C22×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C22×C3 | |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33516 |
3756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 501);