Finite Group DatabasebetaFinite Group Databasebeta| order | 37026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C112 · Schur multiplier (H2) = C11 |
| direct product | C3×C112×D51 |
| unambiguous semidirect product | C3⋊(C3×C112×D17) |
| unambiguous semidirect product | C17⋊(C3×D3×C112) |
| Fitting, socle, Hall | C32×C112×C17 ⋊ C2 |
| derived | C3×C17 ⋊ C2×C3×C112 |
| Hall | C112×C17 ⋊ C3×D3 |
| Hall | C32×C112 ⋊ D17 |
| Hall | C32×C17 ⋊ C2×C112 |
| Sylow | C17 ⋊ C3×D3×C112 |
| Sylow | C32 ⋊ C112×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C112 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C3×C112 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112×C17 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C3×C112 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12342 |
9801 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37026, 58);