Finite Group DatabasebetaFinite Group Databasebeta| order | 33516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C49 · Schur multiplier (H2) = C1 |
| direct product | C9×C49×Dic19 |
| derived, Sylow | C19 ⋊ C4×C9×C49 |
| Hall | C9×C19×C49 ⋊ C4 |
| Hall | C19×C49 ⋊ C4×C9 |
| Hall | C9×C19 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9×C49 | D19 |
| commutator, hypocenter | C19 | C4×C9×C49 |
| Frattini | C2×C3×C7 | C3×C7×D19 |
| Fitting | C2×C9×C19×C49 | C2 |
| socle, prime radical, cosocle | C2×C3×C7×C19 | C2×C3×C7 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C9×C49 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 33516 |
9702 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33516, 18);