Finite Group DatabasebetaFinite Group Databasebeta| order | 11676 |
| isoclinism | isoclinic class of D139 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C7×D139 |
| Fitting, socle | C2×C3×C7×C139 ⋊ C2 |
| derived, Sylow | C139 ⋊ C22×C3×C7 |
| Hall | C3×C7×C139 ⋊ C22 |
| Hall | C7×C139 ⋊ C22×C3 |
| Hall | C3×C139 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D139 |
| commutator, cosocle, hypocenter | C139 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C139 | C2 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C3×C7 | |
40 conjugacy classes of subgroups.
2982 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×D139⋊C9, C2×#31776103, C2×#31776102, … |
| maximal normal subgroup of | C2×C7×D139⋊C9, C2×#31776103, C2×#31776102, … |
| maximal quotient of | C2×C7×C9×D139, C3×D3×C7×D139, C2×C32×C7×D139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11676, 64);