Finite Group DatabasebetaFinite Group Databasebeta| order | 37122 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C269 · Schur multiplier (H2) = C1 |
| direct product | C3×D23×C269 |
| unambiguous semidirect product | C23⋊(C2×C3×C269) |
| Fitting, socle, Hall | C3×C23×C269 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C3×C269 |
| Hall | C23×C269 ⋊ C2×C3 |
| Hall | C3×C23 ⋊ C2×C269 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C269 | D23 |
| commutator, cosocle, hypocenter | C23 | C2×C3×C269 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C269 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C269 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18561 |
10491 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37122, 3);