Finite Group DatabasebetaFinite Group Databasebeta| order | 29766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#10624391 |
| Fitting, socle, Hall | C112×C41 ⋊ D3 |
| derived, Hall | C112⋊C3 ⋊ C2×C41 |
| Hall | C41×C112⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ D3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #10624391 |
| commutator, cosocle, hypocenter | C112⋊C3 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C112×C41 | D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C41 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1353 |
1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29766, 11);