Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C37 |
| unambiguous semidirect product | C3⋊(C3⋊(C37⋊D37)) |
| unambiguous semidirect product | C37⋊(C3⋊D111) |
| Fitting, socle, derived, Hall | C32×C372 ⋊ C2 |
| Sylow | C372 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ C37⋊D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C372 | C2 |
| LCS | G ▷ C32×C372 | |
| UCS | C1 | |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12321 |
Polycyclic presentation:
2,3^2,37^2|b^a=b^2,c^a=c^2,d^a=d^36,e^a=e^366162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 97);