Finite Group DatabasebetaFinite Group Databasebeta| order | 11868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D989 |
| unambiguous semidirect product | (D3×C23)⋊D43 |
| unambiguous semidirect product | (D3×C43)⋊D23 |
| Fitting, socle, derived, Hall | C3×C23×C43 ⋊ C22 |
| Hall | C23×C43 ⋊ C2×D3 |
| Hall | C3×C43 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ C2×D43 |
| Sylow | C43 ⋊ D3×D23 |
| Sylow | C23 ⋊ D3×D43 |
| Sylow | C3 ⋊ C2×D989 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C23×C43 | C22 |
| LCS | G ▷ C3×C23×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
1488 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D989, D3×C23⋊(D43⋊C3), C3×D3×D989, … |
| maximal normal subgroup of | D3×C23⋊(D43⋊C3), C3×D3×D989 |
| maximal quotient of | D9×D989, C3×D3×D989, D3×D2967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11868, 23);