Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D4107 |
| unambiguous semidirect product | C1369⋊(C3⋊D3) |
| Fitting, derived, Hall | C32×C1369 ⋊ C2 |
| Sylow | C1369 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D1369 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C1369 | C2 |
| Frattini | C37 | C3⋊D111 |
| socle | C32×C37 | D37 |
| LCS | G ▷ C32×C1369 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12321 |
Polycyclic presentation:
2,3^2,37^2|d^37=e^36,b^a=b^2,c^a=c^2,d^a=d^36e,e^a=e^366162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 18);