Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #31822415⋊C2 |
| unambiguous semidirect product | #31822419⋊C2 |
| unambiguous semidirect product | #31822423⋊C2 |
| Fitting, derived, Hall | C49×C61 ⋊ C22×C3 |
| Hall | D49×D61 ⋊ C3 |
| Hall | #22582218 ⋊ C22 |
| Sylow | C61 ⋊ C2×D49⋊C3 |
| Sylow | C49 ⋊ C2×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C61 | C22×C3 |
| Frattini | C7 | #14579420⋊C2 |
| socle | C7×C61 | C2×AGL(1,𝔽7) |
| LCS | G ▷ C49×C61 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2989 |
Polycyclic presentation:
2^2,3,7,61,7|d^7=f^6,e^a=e^60,d^b=d^6f,f^b=f^6,d^c=d^2f^3,e^c=e^47,f^c=f^2288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 30);