Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D4107 |
| unambiguous semidirect product | C3⋊(C3×D1369) |
| Fitting, Hall | C32×C1369 ⋊ C2 |
| derived | C3×C1369 ⋊ C2×C3 |
| Sylow | C1369 ⋊ C3×D3 |
| Sylow | C32 ⋊ D1369 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D4107 |
| commutator, cosocle, hypocenter | C3×C1369 | C2×C3 |
| Frattini | C37 | C3×D111 |
| Fitting | C32×C1369 | C2 |
| socle | C32×C37 | D37 |
| LCS | G ▷ C3×C1369 | |
| UCS | C1 ◁ C3 | |
27 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8214 |
6165 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 16);