Finite Group DatabasebetaFinite Group Databasebeta| order | 16562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C13⋊D637 |
| unambiguous semidirect product | C49⋊(C13⋊D13) |
| Fitting, derived, Hall | C132×C49 ⋊ C2 |
| Sylow | C132 ⋊ D49 |
| Sylow | C49 ⋊ C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C132×C49 | C2 |
| Frattini | C7 | C7⋊(C13⋊D13) |
| socle | C7×C132 | D7 |
| LCS | G ▷ C132×C49 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
Polycyclic presentation:
2,7,13^2,7|b^7=e^6,b^a=b^6e,c^a=c^12,d^a=d^12,e^a=e^64142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×C13⋊D13, D13×D637, C2×C13⋊D637 |
| maximal normal subgroup of | D49×C13⋊D13, D13×D637, C2×C13⋊D637 |
| maximal quotient of | C49⋊#10621725, C2×C13⋊D637 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16562, 19);