Finite Group DatabasebetaFinite Group Databasebeta| order | 29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C67⋊#3866 |
| Fitting, socle, Hall | C3×C37×C67 ⋊ C4 |
| derived, Hall | C37×C67 ⋊ C3×C4 |
| Hall | C3×C67 ⋊ #3866 |
| Hall | C3×C37 ⋊ Dic67 |
| Sylow | C67 ⋊ C3×#3866 |
| Sylow | C37 ⋊ C3×Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C67⋊#3866 |
| commutator, hypocenter | C37×C67 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C67 | C4 |
| prime radical | C3×C67×D37 | C2 |
| cosocle | C67×D37 | C2×C3 |
| LCS | G ▷ C37×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7437 |
2019 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29748, 51);