Finite Group DatabasebetaFinite Group Databasebeta| order | 13786 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×D61 |
| unambiguous semidirect product | C61⋊(C2×C113) |
| Fitting, socle, Hall | C61×C113 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | D61 |
| commutator, cosocle, hypocenter | C61 | C2×C113 |
| Frattini | C1 | G |
| Fitting, socle | C61×C113 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C113 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6893 |
3616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C113×#6923, #42118431, D61×D113, … |
| maximal normal subgroup of | C113×#6923, #42118431, D61×D113, … |
| maximal quotient of | C113×Dic61, C2×C113×D61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13786, 1);