Finite Group DatabasebetaFinite Group Databasebeta| order | 35844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C29⋊(D103⋊C3) |
| unambiguous semidirect product | (C2×C29)⋊(D103⋊C3) |
| unambiguous semidirect product | (C2×C103⋊C3)⋊D29 |
| unambiguous semidirect product | (C2×D2987)⋊C3 |
| Fitting, socle | C2×C29×C103 ⋊ C2×C3 |
| derived, Hall | C29×C103 ⋊ C22×C3 |
| Hall | C2×D2987 ⋊ C3 |
| Hall | C29×C103⋊C3 ⋊ C22 |
| Hall | C103⋊C3 ⋊ C2×D29 |
| Sylow | C103 ⋊ C2×C3×D29 |
| Sylow | C29 ⋊ C2×D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C29⋊(D103⋊C3) |
| commutator, cosocle, hypocenter | C29×C103 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C103 | C2×C3 |
| LCS | G ▷ C29×C103 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5974 |
1082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35844, 18);