Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C29×D29 |
| unambiguous semidirect product | C29⋊(C22×C3×C29) |
| unambiguous semidirect product | (C2×C29)⋊(C2×C3×C29) |
| Fitting, socle | C2×C3×C292 ⋊ C2 |
| derived | C29 ⋊ C22×C3×C29 |
| Hall | C3×C292 ⋊ C22 |
| Sylow | C292 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C29 | D29 |
| commutator, cosocle, hypocenter | C29 | C22×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C292 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C3×C29 | |
96 conjugacy classes of subgroups.
2784 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×C29×D29, C2×C3×#19097943, C3×D3×C29×D29, … |
| maximal normal subgroup of | C2×C9×C29×D29, C2×C32×C29×D29 |
| maximal quotient of | C2×C9×C29×D29, C3×D3×C29×D29, C2×C32×C29×D29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 48);