Finite Group DatabasebetaFinite Group Databasebeta| order | 37479 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C312 · Schur multiplier (H2) = C31 |
| direct product | C312×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C312) |
| Fitting, socle, Hall | C13×C312 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C312 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C312 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C312 |
| Frattini | C1 | G |
| Fitting, socle | C13×C312 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C312 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12493 |
6727 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37479, 10);