Finite Group DatabasebetaFinite Group Databasebeta| order | 18762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×D159 |
| unambiguous semidirect product | C3⋊(C59×D53) |
| unambiguous semidirect product | C53⋊(D3×C59) |
| Fitting, socle, Hall | C3×C53×C59 ⋊ C2 |
| derived, Hall | C3×C53 ⋊ C2×C59 |
| Hall | C53×C59 ⋊ D3 |
| Hall | C3×C59 ⋊ D53 |
| Sylow | C53 ⋊ D3×C59 |
| Sylow | C3 ⋊ C59×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | D159 |
| commutator, cosocle, hypocenter | C3×C53 | C2×C59 |
| Frattini | C1 | G |
| Fitting, socle | C3×C53×C59 | C2 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C59 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9381 |
4779 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D159, D3×C59×D53, D159⋊D59, … |
| maximal normal subgroup of | D59×D159, D3×C59×D53, D159⋊D59, … |
| maximal quotient of | C59×Dic159, C2×C59×D159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18762, 7);