Finite Group DatabasebetaFinite Group Databasebeta| order | 13786 |
| isoclinism | isoclinic class of D113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D113 |
| unambiguous semidirect product | C113⋊(C2×C61) |
| Fitting, socle, Hall | C61×C113 ⋊ C2 |
| derived, Sylow | C113 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D113 |
| commutator, cosocle, hypocenter | C113 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C61×C113 | C2 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C61 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6893 |
3538 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C61×#90673, #42118432, D61×D113, … |
| maximal normal subgroup of | C61×#90673, #42118432, D61×D113, … |
| maximal quotient of | C61×Dic113, C2×C61×D113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13786, 2);