Finite Group DatabasebetaFinite Group Databasebeta| order | 23052 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1921 |
| unambiguous semidirect product | (D3×C17)⋊D113 |
| unambiguous semidirect product | (D3×C113)⋊D17 |
| Fitting, socle, derived, Hall | C3×C17×C113 ⋊ C22 |
| Hall | C17×C113 ⋊ C2×D3 |
| Hall | C3×C113 ⋊ C2×D17 |
| Sylow | C113 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×D113 |
| Sylow | C17 ⋊ D3×D113 |
| Sylow | C3 ⋊ C2×D1921 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C113 | C22 |
| LCS | G ▷ C3×C17×C113 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5763 |
2886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23052, 27);