Finite Group DatabasebetaFinite Group Databasebeta| order | 11676 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×Dic139 |
| derived, Sylow | C139 ⋊ C3×C4×C7 |
| Hall | C3×C7×C139 ⋊ C4 |
| Hall | C7×C139 ⋊ C3×C4 |
| Hall | C3×C139 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D139 |
| commutator, hypocenter | C139 | C3×C4×C7 |
| Frattini | C2 | C3×C7×D139 |
| Fitting, socle, prime radical | C2×C3×C7×C139 | C2 |
| cosocle | C2×C139 | C2×C3×C7 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C3×C7 | |
24 conjugacy classes of subgroups.
2982 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C9×Dic139, C7×Dic139⋊C9, C7⋊C9×Dic139, … |
| maximal normal subgroup of | C7×C9×Dic139, C7×Dic139⋊C9, C7⋊C9×Dic139, … |
| maximal quotient of | C7×C9×Dic139, C3×C7×Dic417, C32×C7×Dic139 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11676, 6);