Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D3×C29×D29 |
| unambiguous semidirect product | (D3×C29)⋊(C2×C29) |
| unambiguous semidirect product | (C3×D29)⋊(C2×C29) |
| unambiguous semidirect product | D87⋊(C2×C29) |
| Fitting, socle, Hall | C3×C292 ⋊ C22 |
| derived | C3×C29 ⋊ C22×C29 |
| Sylow | C292 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×C29×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D3×D29 |
| commutator, cosocle, hypocenter | C3×C29 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C292 | C22 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C29 | |
96 conjugacy classes of subgroups.
1392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×C29×D29, D3×#19097943, C3×D3×C29×D29, … |
| maximal normal subgroup of | C3×D3×C29×D29 |
| maximal quotient of | D9×C29×D29, C3×D3×C29×D29, D3×C29×D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 34);