Finite Group DatabasebetaFinite Group Databasebeta| order | 29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C67⋊#3866) |
| unambiguous semidirect product | C67⋊(C3⋊#3866) |
| Fitting, socle, derived, Hall | C3×C37×C67 ⋊ C4 |
| Hall | C37×C67 ⋊ Dic3 |
| Hall | C3×C67 ⋊ #3866 |
| Hall | C3×C37 ⋊ Dic67 |
| Sylow | C67 ⋊ C3⋊#3866 |
| Sylow | C37 ⋊ Dic201 |
| Sylow | C3 ⋊ C67⋊#3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C37×C67 | C4 |
| prime radical, cosocle | C3×C67×D37 | C2 |
| LCS | G ▷ C3×C37×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7437 |
Polycyclic presentation:
2^2,3,37,67|a^2=b,c^a=c^2,d^a=d^31,e^a=e^66,d^b=d^362013 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29748, 55);