Finite Group DatabasebetaFinite Group Databasebeta| order | 37539 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C43 · Schur multiplier (H2) = C3 |
| direct product | C3×C43×C97⋊C3 |
| unambiguous semidirect product | C97⋊(C32×C43) |
| unambiguous semidirect product | (C3×C97)⋊(C3×C43) |
| Fitting, socle | C3×C43×C97 ⋊ C3 |
| derived, Sylow | C97 ⋊ C32×C43 |
| Hall | C43×C97 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | C97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C32×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C43×C97 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C43 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12513 |
4515 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37539, 8);