Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D292 |
| unambiguous semidirect product | (C29×D29)⋊(C2×C3) |
| Fitting, socle, Hall | C3×C292 ⋊ C22 |
| derived, Sylow | C292 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D292 |
| commutator, cosocle, hypocenter | C292 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C292 | C22 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
768 conjugacy classes — view the full character table.
| maximal subgroup of | C9×D292, C3×#19097943⋊C2, C32×D292, … |
| maximal normal subgroup of | C9×D292, C32×D292 |
| maximal quotient of | C9×D292, C32×D292, C3×D29×D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 32);