Finite Group DatabasebetaFinite Group Databasebeta| order | 26871 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived | C13×C53 ⋊ C3×C13 |
| Hall | C13×C53⋊C13 ⋊ C3 |
| Sylow | C53 ⋊ C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C53 | C3×C13 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 689 |
119 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26871, 5);