Finite Group DatabasebetaFinite Group Databasebeta| order | 14415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C961⋊C3 |
| unambiguous semidirect product | (C5×C961)⋊C3 |
| Fitting, Hall | C5×C961 ⋊ C3 |
| derived, Sylow | C961 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C961⋊C3 |
| commutator, cosocle, hypocenter | C961 | C3×C5 |
| Frattini | C31 | C5×C31⋊C3 |
| Fitting | C5×C961 | C3 |
| socle | C5×C31 | C31⋊C3 |
| LCS | G ▷ C961 | |
| UCS | C1 ◁ C5 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4805 |
1615 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D961⋊C3, D5×C961⋊C3, C5⋊(D961⋊C3), … |
| maximal normal subgroup of | C5×D961⋊C3, D5×C961⋊C3, C5⋊(D961⋊C3), … |
| maximal quotient of | C2×C5×C961⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14415, 4);