Finite Group DatabasebetaFinite Group Databasebeta| order | 13706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×C89⋊C11 |
| unambiguous semidirect product | (C2×C89)⋊(C7×C11) |
| unambiguous semidirect product | (C2×C7×C89)⋊C11 |
| Fitting, socle, Hall | C2×C7×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C2×C7×C11 |
| Hall | C7×C89 ⋊ C2×C11 |
| Hall | C2×C89 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C89⋊C11 |
| commutator, cosocle, hypocenter | C89 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1246 |
266 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C7×C89⋊C11, C7×Dic89⋊C11, Dic7×C89⋊C11, … |
| maximal normal subgroup of | C4×C7×C89⋊C11, C7×Dic89⋊C11, Dic7×C89⋊C11, … |
| maximal quotient of | C4×C7×C89⋊C11, C22×C7×C89⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13706, 2);