Finite Group DatabasebetaFinite Group Databasebeta| order | 17526 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C127 · Schur multiplier (H2) = C1 |
| direct product | C127×D69 |
| unambiguous semidirect product | C3⋊(D23×C127) |
| unambiguous semidirect product | C23⋊(D3×C127) |
| Fitting, socle, Hall | C3×C23×C127 ⋊ C2 |
| derived, Hall | C3×C23 ⋊ C2×C127 |
| Hall | C23×C127 ⋊ D3 |
| Hall | C3×C127 ⋊ D23 |
| Sylow | C23 ⋊ D3×C127 |
| Sylow | C3 ⋊ D23×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | D69 |
| commutator, cosocle, hypocenter | C3×C23 | C2×C127 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C127 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C127 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8763 |
4572 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D69×D127, D3×D23×C127, D69⋊D127, … |
| maximal normal subgroup of | D69×D127, D3×D23×C127, D69⋊D127, … |
| maximal quotient of | C127×Dic69, C2×C127×D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17526, 8);