Finite Group DatabasebetaFinite Group Databasebeta| order | 17526 |
| isoclinism | isoclinic class of D127 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×D127 |
| Fitting, socle, Hall | C3×C23×C127 ⋊ C2 |
| derived, Sylow | C127 ⋊ C2×C3×C23 |
| Hall | C23×C127 ⋊ C2×C3 |
| Hall | C3×C127 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | D127 |
| commutator, cosocle, hypocenter | C127 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C127 | C2 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C3×C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8763 |
4485 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D127, D3×C23×D127, D69×D127, … |
| maximal normal subgroup of | C3×D23×D127, D3×C23×D127, D69×D127, … |
| maximal quotient of | C3×C23×Dic127, C2×C3×C23×D127 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17526, 3);