Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic2989 |
| derived, Hall | C49×C61 ⋊ C3×C4 |
| Hall | C3×C49×C61 ⋊ C4 |
| Hall | C3×C61 ⋊ Dic49 |
| Hall | C3×C49 ⋊ Dic61 |
| Sylow | C61 ⋊ C3×Dic49 |
| Sylow | C49 ⋊ C3×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D2989 |
| commutator, hypocenter | C49×C61 | C3×C4 |
| Frattini | C2×C7 | C3×D427 |
| Fitting | C2×C3×C49×C61 | C2 |
| socle, prime radical | C2×C3×C7×C61 | D7 |
| cosocle | C2×C49×C61 | C2×C3 |
| LCS | G ▷ C49×C61 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 35868 |
8976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 8);