Finite Group DatabasebetaFinite Group Databasebeta| order | 26169 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#14558651 |
| Fitting, socle, Hall | C11×C13×C61 ⋊ C3 |
| derived, Hall | C13×C61 ⋊ C3×C11 |
| Hall | C11×C61 ⋊ C13⋊C3 |
| Hall | C11×C13 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C11×C13⋊C3 |
| Sylow | C13 ⋊ C11×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #14558651 |
| commutator, cosocle, hypocenter | C13×C61 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C61 | C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8723 |
2937 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26169, 5);