Finite Group DatabasebetaFinite Group Databasebeta| order | 36754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C23 · Schur multiplier (H2) = C1 |
| direct product | C17×AGL(1,𝔽47) |
| unambiguous semidirect product | D47⋊(C17×C23) |
| unambiguous semidirect product | (C47⋊C23)⋊(C2×C17) |
| unambiguous semidirect product | (C17×D47)⋊C23 |
| Fitting, socle, Hall | C17×C47 ⋊ C2×C23 |
| derived, Sylow | C47 ⋊ C2×C17×C23 |
| Hall | C17×C47⋊C23 ⋊ C2 |
| Hall | C17×D47 ⋊ C23 |
| Hall | C47⋊C23 ⋊ C2×C17 |
| Hall | D47 ⋊ C17×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | AGL(1,𝔽47) |
| commutator, cosocle, hypocenter | C47 | C2×C17×C23 |
| Frattini | C1 | G |
| Fitting, socle | C17×C47 | C2×C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 799 |
799 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36754, 10);