Finite Group DatabasebetaFinite Group Databasebeta| order | 37998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D2111 |
| unambiguous semidirect product | C2111⋊(C2×C9) |
| Fitting, Hall | C9×C2111 ⋊ C2 |
| derived, Sylow | C2111 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D2111 |
| commutator, hypocenter | C2111 | C2×C9 |
| Frattini | C3 | C3×D2111 |
| Fitting | C9×C2111 | C2 |
| socle, cosocle | C3×C2111 | C2×C3 |
| prime radical | C3×D2111 | C3 |
| LCS | G ▷ C2111 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18999 |
9513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37998, 3);