Finite Group DatabasebetaFinite Group Databasebeta| order | 6052 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D89 |
| unambiguous semidirect product | (D17×C89)⋊C2 |
| unambiguous semidirect product | (C17×D89)⋊C2 |
| unambiguous semidirect product | D1513⋊C2 |
| Fitting, socle, derived, Hall | C17×C89 ⋊ C22 |
| Sylow | C89 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C89 | C22 |
| LCS | G ▷ C17×C89 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
460 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D17×D89, D51×D89, D17×D267, … |
| maximal normal subgroup of | C3×D17×D89, C5×D17×D89 |
| maximal quotient of | C3×D17×D89, D51×D89, D17×D267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6052, 12);