Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| direct product | C5⋊D5×C31⋊C9 |
| unambiguous semidirect product | C5⋊(D5×C31⋊C9) |
| derived, Hall | C52×C31 ⋊ C2×C9 |
| Hall | C52×C31⋊C9 ⋊ C2 |
| Hall | C31×C5⋊D5 ⋊ C9 |
| Sylow | C31 ⋊ C9×C5⋊D5 |
| Sylow | C52 ⋊ C2×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊D5×C31⋊C3 |
| commutator, hypocenter | C52×C31 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C31 | C2×C3 |
| prime radical | C3×C31×C5⋊D5 | C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
546 conjugacy classes — view the full character table.
| maximal subgroup of | (C31⋊C9)⋊#1043, #1043×C31⋊C9, (C31⋊C9)⋊#1044, … |
| maximal normal subgroup of | (C31⋊C9)⋊#1043, #1043×C31⋊C9, (C31⋊C9)⋊#1044, … |
| maximal quotient of | #1039×C31⋊C9, C2×C5⋊D5×C31⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 65);