Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| isoclinism | isoclinic class of C13⋊D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C13 |
| direct product | C49×C13⋊D13 |
| unambiguous semidirect product | C13⋊(D13×C49) |
| Fitting, Hall | C132×C49 ⋊ C2 |
| derived, Sylow | C132 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C13⋊D13 |
| commutator, hypocenter | C132 | C2×C49 |
| Frattini | C7 | C7×C13⋊D13 |
| Fitting | C132×C49 | C2 |
| socle, cosocle | C7×C132 | C2×C7 |
| prime radical | C7×C13⋊D13 | C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C49 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
4214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C49×#10621728, C49×#10621729, D132×C49, … |
| maximal normal subgroup of | C49×#10621728, C49×#10621729, D132×C49, … |
| maximal quotient of | C49×#10621725, C2×C49×C13⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 16);