Finite Group DatabasebetaFinite Group Databasebeta| order | 25986 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1 |
| direct product | C3×C71×D61 |
| Fitting, socle, Hall | C3×C61×C71 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C3×C71 |
| Hall | C61×C71 ⋊ C2×C3 |
| Hall | C3×C61 ⋊ C2×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C71 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C61×C71 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12993 |
6816 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25986, 4);