Finite Group DatabasebetaFinite Group Databasebeta| order | 8606 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C331 · Schur multiplier (H2) = C1 |
| direct product | D13×C331 |
| unambiguous semidirect product | C13⋊(C2×C331) |
| Fitting, socle, Hall | C13×C331 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C331 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C331 | D13 |
| commutator, hypocenter | C13 | C2×C331 |
| Frattini | C1 | G |
| Fitting, socle | C13×C331 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C331 | |
8 conjugacy classes of subgroups.
2648 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #261×C331, C331⋊#261, D13×D331, … |
| maximal normal subgroup of | #261×C331, C331⋊#261, D13×D331, … |
| maximal quotient of | Dic13×C331, C2×D13×C331, C3×D13×C331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8606, 1);