Finite Group DatabasebetaFinite Group Databasebeta| order | 10092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D841 |
| unambiguous semidirect product | (D3×C841)⋊C2 |
| unambiguous semidirect product | (C3×D841)⋊C2 |
| unambiguous semidirect product | D2523⋊C2 |
| Fitting, derived, Hall | C3×C841 ⋊ C22 |
| Sylow | C841 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D841 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C841 | C22 |
| Frattini | C29 | D3×D29 |
| socle | C3×C29 | C2×D29 |
| LCS | G ▷ C3×C841 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
1266 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D841, C3×D3×D841, C3⋊D3×D841, … |
| maximal normal subgroup of | C3×D3×D841 |
| maximal quotient of | D9×D841, C3×D3×D841, C3⋊D3×D841, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10092, 8);