Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #27134456⋊C2 |
| Fitting, derived, Sylow | C1369 ⋊ C2×C9 |
| Hall | #27134456 ⋊ C2 |
| Hall | D1369 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C1369 | C2×C9 |
| Frattini, socle | C37 | #66526⋊C2 |
| prime radical | D1369⋊C3 | C3 |
| cosocle | C1369⋊C3 | C2×C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1369 |
Polycyclic presentation:
2,3^2,37^2|b^3=c,d^37=e^36,d^a=d^36e,e^a=e^36,d^b=d^16e^10,e^b=e^16,d^c=d^26e^22,e^c=e^2694 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 8);