Finite Group DatabasebetaFinite Group Databasebeta| order | 26847 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C157 · Schur multiplier (H2) = C3 |
| direct product | C3×C19⋊C3×C157 |
| unambiguous semidirect product | C19⋊(C32×C157) |
| unambiguous semidirect product | (C3×C19)⋊(C3×C157) |
| Fitting, socle | C3×C19×C157 ⋊ C3 |
| derived, Sylow | C19 ⋊ C32×C157 |
| Hall | C19×C157 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C157 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C32×C157 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C157 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C157 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8949 |
4239 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26847, 12);