Finite Group DatabasebetaFinite Group Databasebeta| order | 35916 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic73⋊C3 |
| unambiguous semidirect product | Dic73⋊(C3×C41) |
| unambiguous semidirect product | (C41×Dic73)⋊C3 |
| derived, Sylow | C73 ⋊ C3×C4×C41 |
| Hall | C41×Dic73 ⋊ C3 |
| Hall | C41×C73⋊C3 ⋊ C4 |
| Hall | C41×C73 ⋊ C3×C4 |
| Hall | Dic73 ⋊ C3×C41 |
| Hall | C73⋊C3 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D73⋊C3 |
| commutator, hypocenter | C73 | C3×C4×C41 |
| Frattini | C2 | C41×D73⋊C3 |
| Fitting, socle | C2×C41×C73 | C2×C3 |
| prime radical | C2×C41×C73⋊C3 | C2 |
| cosocle | C2×C73 | C2×C3×C41 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C41 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11972 |
1476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35916, 10);