Finite Group DatabasebetaFinite Group Databasebeta| order | 26871 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C169⋊C3 |
| unambiguous semidirect product | C169⋊(C3×C53) |
| unambiguous semidirect product | (C53×C169)⋊C3 |
| Fitting, Hall | C53×C169 ⋊ C3 |
| derived, Sylow | C169 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | C169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C3×C53 |
| Frattini | C13 | C13⋊C3×C53 |
| Fitting | C53×C169 | C3 |
| socle | C13×C53 | C13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C53 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8957 |
3127 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26871, 3);