Finite Group DatabasebetaFinite Group Databasebeta| order | 26847 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#22582161 |
| Fitting, socle | C3×C19×C157 ⋊ C3 |
| derived, Hall | C19×C157 ⋊ C32 |
| Sylow | C157 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #22582161 |
| commutator, cosocle, hypocenter | C19×C157 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C157 | C3 |
| LCS | G ▷ C19×C157 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8949 |
2991 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26847, 13);