Finite Group DatabasebetaFinite Group Databasebeta| order | 14415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C961⋊C3)⋊C5 |
| unambiguous semidirect product | (C961⋊C5)⋊C3 |
| Fitting, derived, Sylow | C961 ⋊ C3×C5 |
| Hall | C961⋊C5 ⋊ C3 |
| Hall | C961⋊C3 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C961 | C3×C5 |
| Frattini, socle | C31 | (C31⋊C3)⋊C5 |
| LCS | G ▷ C961 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 961 |
Polycyclic presentation:
3,5,31^2|c^31=d^2,c^a=c^25d,d^a=d^25,c^b=c^16d^24,d^b=d^1679 conjugacy classes — view the full character table.
| maximal subgroup of | (D961⋊C3)⋊C5, C2×(C961⋊C3)⋊C5 |
| maximal normal subgroup of | (D961⋊C3)⋊C5, C2×(C961⋊C3)⋊C5 |
| maximal quotient of | C2×(C961⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14415, 2);