Finite Group DatabasebetaFinite Group Databasebeta| order | 35868 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C61⋊C3×#5997 |
| Fitting, socle, derived, Hall | C72×C61 ⋊ C3×C4 |
| Hall | C61×#5997 ⋊ C3 |
| Hall | C72×C61⋊C3 ⋊ C4 |
| Sylow | C61 ⋊ C3×#5997 |
| Sylow | C72 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C61 | C3×C4 |
| prime radical | C7⋊D7×C61⋊C3 | C2 |
| cosocle | C61×C7⋊D7 | C2×C3 |
| LCS | G ▷ C72×C61 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 854 |
368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35868, 156);