Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D427⋊D21 |
| Fitting, socle, derived, Hall | C3×C72×C61 ⋊ C22 |
| Hall | C72×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ D72 |
| Hall | C3×C72 ⋊ C2×D61 |
| Sylow | C61 ⋊ D7×D21 |
| Sylow | C72 ⋊ D3×D61 |
| Sylow | C3 ⋊ (C7⋊D7)⋊D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C61 | C22 |
| LCS | G ▷ C3×C72×C61 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2562 |
Polycyclic presentation:
2^2,3,7^2,61|d^a=d^6,f^a=f^60,c^b=c^2,d^b=d^6,e^b=e^62310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 338);