Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C1369 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C1369 |
| unambiguous semidirect product | C3⋊(D3×C1369) |
| Fitting, Hall | C32×C1369 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C1369 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1369 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C1369 |
| Frattini | C37 | C3⋊D3×C37 |
| Fitting | C32×C1369 | C2 |
| socle, cosocle | C32×C37 | C2×C37 |
| prime radical | C3⋊D3×C37 | C37 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C1369 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12321 |
8214 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 17);