Finite Group DatabasebetaFinite Group Databasebeta| order | 1998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #11758608⋊C2 |
| Hall | #11758608 ⋊ C2 |
| Hall | D37 ⋊ 3−1+2 |
| Sylow | C37 ⋊ C2×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×D37⋊C3 |
| commutator, socle, cosocle | C3×C37 | C2×C32 |
| Fitting | C32×C37 | C2×C3 |
| prime radical | C32×D37 | C3 |
| hypercenter | C32 | D37⋊C3 |
| hypocenter | C37 | C2×3−1+2 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3 ◁ C32 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
Polycyclic presentation:
2,3^3,37|b^3=d,e^a=e^36,c^b=cd,e^b=e^1076 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1998, 13);