Finite Group DatabasebetaFinite Group Databasebeta| order | 14514 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×D123 |
| unambiguous semidirect product | C3⋊(C59×D41) |
| unambiguous semidirect product | C41⋊(D3×C59) |
| Fitting, socle, Hall | C3×C41×C59 ⋊ C2 |
| derived, Hall | C3×C41 ⋊ C2×C59 |
| Hall | C41×C59 ⋊ D3 |
| Hall | C3×C59 ⋊ D41 |
| Sylow | C41 ⋊ D3×C59 |
| Sylow | C3 ⋊ C59×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | D123 |
| commutator, cosocle, hypocenter | C3×C41 | C2×C59 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C59 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C59 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7257 |
3717 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D123, D3×C59×D41, D123⋊D59, … |
| maximal normal subgroup of | D59×D123, D3×C59×D41, D123⋊D59, … |
| maximal quotient of | C59×Dic123, C2×C59×D123 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14514, 7);