Finite Group DatabasebetaFinite Group Databasebeta| order | 17565 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C1171⋊C3)⋊C5 |
| unambiguous semidirect product | (C1171⋊C5)⋊C3 |
| Fitting, socle, derived, Sylow | C1171 ⋊ C3×C5 |
| Hall | C1171⋊C5 ⋊ C3 |
| Hall | C1171⋊C3 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1171 | C3×C5 |
| LCS | G ▷ C1171 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1171 |
Polycyclic presentation:
3,5,1171|c^a=c^420,c^b=c^7093 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C1171⋊C3)⋊C5, (D1171⋊C3)⋊C5 |
| maximal normal subgroup of | C2×(C1171⋊C3)⋊C5, (D1171⋊C3)⋊C5 |
| maximal quotient of | C2×(C1171⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17565, 1);