Finite Group DatabasebetaFinite Group Databasebeta| order | 16614 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊(D13⋊C9) |
| unambiguous semidirect product | (C13⋊C9)⋊D71 |
| unambiguous semidirect product | D923⋊C9 |
| derived, Hall | C13×C71 ⋊ C2×C9 |
| Hall | C71×C13⋊C9 ⋊ C2 |
| Hall | D923 ⋊ C9 |
| Hall | C13⋊C9 ⋊ D71 |
| Sylow | C71 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ C9×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C13⋊C3)⋊D71 |
| commutator, hypocenter | C13×C71 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C71 | C2×C3 |
| prime radical | C3×D923 | C3 |
| LCS | G ▷ C13×C71 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8307 |
Polycyclic presentation:
2,3,13,71,3|b^3=e,c^a=c^12,d^a=d^70,c^b=c^3759 conjugacy classes — view the full character table.
| maximal subgroup of | D71×D13⋊C9, C2×C71⋊(D13⋊C9) |
| maximal normal subgroup of | D71×D13⋊C9, C2×C71⋊(D13⋊C9) |
| maximal quotient of | C71⋊(Dic13⋊C9), C2×C71⋊(D13⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16614, 12);