Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1369 |
| Fitting, Hall | C9×C1369 ⋊ C2 |
| derived, Sylow | C1369 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1369 |
| commutator, hypocenter | C1369 | C2×C9 |
| Frattini, socle | C3×C37 | C3×D37 |
| Fitting | C9×C1369 | C2 |
| prime radical | C3×D1369 | C3 |
| cosocle | C3×C1369 | C2×C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C9 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12321 |
6174 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 5);