Finite Group DatabasebetaFinite Group Databasebeta| order | 23052 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×C3⋊#595 |
| unambiguous semidirect product | C3⋊(#595×C113) |
| Fitting, socle, Hall | C3×C17×C113 ⋊ C4 |
| derived, Hall | C3×C17 ⋊ C4×C113 |
| Hall | C17×C113 ⋊ Dic3 |
| Hall | C3×C113 ⋊ #595 |
| Sylow | C17 ⋊ Dic3×C113 |
| Sylow | C3 ⋊ #595×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | C3⋊#595 |
| commutator, hypocenter | C3×C17 | C4×C113 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C113 | C4 |
| prime radical | C3×D17×C113 | C2 |
| cosocle | C3×D17 | C2×C113 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C113 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5763 |
2034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23052, 19);