Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C49×C61 ⋊ C22×C3 |
| Hall | D49×D61 ⋊ C3 |
| Hall | C49×C61⋊C3 ⋊ C22 |
| Hall | C61⋊C3 ⋊ C2×D49 |
| Sylow | C61 ⋊ C2×C3×D49 |
| Sylow | C49 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C61 | C22×C3 |
| Frattini | C7 | D7×D61⋊C3 |
| socle | C7×C61 | C2×C3×D7 |
| LCS | G ▷ C49×C61 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2989 |
416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 37);