Finite Group DatabasebetaFinite Group Databasebeta| order | 35916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D41×C73⋊C3 |
| unambiguous semidirect product | C41⋊(C22×C73⋊C3) |
| unambiguous semidirect product | (C2×C41)⋊(C2×C73⋊C3) |
| unambiguous semidirect product | (C2×C73×D41)⋊C3 |
| Fitting, socle | C2×C41×C73 ⋊ C2×C3 |
| derived, Hall | C41×C73 ⋊ C22×C3 |
| Hall | C2×C73×D41 ⋊ C3 |
| Hall | C41×C73⋊C3 ⋊ C22 |
| Sylow | C73 ⋊ C2×C3×D41 |
| Sylow | C41 ⋊ C22×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D41×C73⋊C3 |
| commutator, cosocle, hypocenter | C41×C73 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41×C73 | C2×C3 |
| LCS | G ▷ C41×C73 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5986 |
1188 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35916, 23);