Finite Group DatabasebetaFinite Group Databasebeta| order | 6996 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic159 |
| unambiguous semidirect product | C3⋊(C11×Dic53) |
| derived, Hall | C3×C53 ⋊ C4×C11 |
| Hall | C3×C11×C53 ⋊ C4 |
| Hall | C11×C53 ⋊ Dic3 |
| Sylow | C53 ⋊ C11×Dic3 |
| Hall | C3×C11 ⋊ Dic53 |
| Sylow | C3 ⋊ C11×Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D159 |
| commutator, hypocenter | C3×C53 | C4×C11 |
| Frattini | C2 | C11×D159 |
| Fitting, socle | C2×C3×C11×C53 | C2 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C2×C11 | |
24 conjugacy classes of subgroups.
1782 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×Dic477, C11×C3⋊Dic159, C3×C11×Dic159, … |
| maximal normal subgroup of | C3×C11×Dic159, C5×C11×Dic159, C11⋊C5×Dic159 |
| maximal quotient of | C11×Dic477, C11×C3⋊Dic159, C3×C11×Dic159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6996, 6);