Finite Group DatabasebetaFinite Group Databasebeta| order | 37506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×ΓL(1,𝔽8)×D47 |
| unambiguous semidirect product | C47⋊(C2×C19×ΓL(1,𝔽8)) |
| unambiguous semidirect product | (C7×D47)⋊(C3×C19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | ΓL(1,𝔽8)×D47 |
| commutator, cosocle, hypocenter | C7×C47 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C47 | C2×C3 |
| LCS | G ▷ C7×C47 | |
| UCS | C1 ◁ C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6251 |
2375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37506, 22);