Finite Group DatabasebetaFinite Group Databasebeta| order | 23754 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D321 |
| unambiguous semidirect product | C3⋊(C37×D107) |
| unambiguous semidirect product | C107⋊(D3×C37) |
| Fitting, socle, Hall | C3×C37×C107 ⋊ C2 |
| derived, Hall | C3×C107 ⋊ C2×C37 |
| Hall | C37×C107 ⋊ D3 |
| Hall | C3×C37 ⋊ D107 |
| Sylow | C107 ⋊ D3×C37 |
| Sylow | C3 ⋊ C37×D107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D321 |
| commutator, cosocle, hypocenter | C3×C107 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C107 | C2 |
| LCS | G ▷ C3×C107 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11877 |
5994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23754, 7);