Finite Group DatabasebetaFinite Group Databasebeta| order | 26871 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C132 · Schur multiplier (H2) = C13 |
| direct product | C3×C13×C53⋊C13 |
| unambiguous semidirect product | C53⋊(C3×C132) |
| unambiguous semidirect product | (C3×C53)⋊C132 |
| unambiguous semidirect product | (C3×C13×C53)⋊C13 |
| Fitting, socle | C3×C13×C53 ⋊ C13 |
| derived, Sylow | C53 ⋊ C3×C132 |
| Hall | C3×C53 ⋊ C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | C53⋊C13 |
| commutator, cosocle, hypocenter | C53 | C3×C132 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C53 | C13 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3×C13 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2067 |
663 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26871, 6);