Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #27134454⋊C2 |
| derived, Sylow | C1369 ⋊ C2×C9 |
| Hall | #27134454 ⋊ C2 |
| Hall | D1369 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1369⋊C3 |
| commutator, hypocenter | C1369 | C2×C9 |
| Frattini, socle | C3×C37 | D37⋊C3 |
| Fitting, cosocle | C3×C1369 | C2×C3 |
| prime radical | C3×D1369 | C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12321 |
Polycyclic presentation:
2,3,37,3,37|b^3=d,c^37=e^36,c^a=c^36e,e^a=e^36,c^b=c^26e^22,e^b=e^26702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 2);