Finite Group DatabasebetaFinite Group Databasebeta| order | 29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×(C67⋊C3)⋊C4 |
| unambiguous semidirect product | (C67⋊C3)⋊(C4×C37) |
| unambiguous semidirect product | Dic67⋊(C3×C37) |
| derived, Sylow | C67 ⋊ C3×C4×C37 |
| Hall | C37×Dic67 ⋊ C3 |
| Hall | C37×C67⋊C3 ⋊ C4 |
| Hall | C37×C67 ⋊ C3×C4 |
| Hall | Dic67 ⋊ C3×C37 |
| Hall | C67⋊C3 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D67⋊C3 |
| commutator, hypocenter | C67 | C3×C4×C37 |
| Frattini | C2 | C37×D67⋊C3 |
| Fitting, socle | C2×C37×C67 | C2×C3 |
| prime radical | C2×C37×C67⋊C3 | C2 |
| cosocle | C2×C67 | C2×C3×C37 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9916 |
1258 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29748, 13);