Finite Group DatabasebetaFinite Group Databasebeta| order | 13950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊D1395 |
| unambiguous semidirect product | C9⋊(C5⋊D155) |
| unambiguous semidirect product | C31⋊(C5⋊D45) |
| Fitting, derived, Hall | C52×C9×C31 ⋊ C2 |
| Hall | C52×C31 ⋊ D9 |
| Hall | C9×C31 ⋊ C5⋊D5 |
| Hall | C52×C9 ⋊ D31 |
| Sylow | C31 ⋊ C5⋊D45 |
| Sylow | C52 ⋊ D279 |
| Sylow | C9 ⋊ C5⋊D155 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C9×C31 | C2 |
| Frattini | C3 | C3⋊(C5⋊D155) |
| socle | C3×C52×C31 | D3 |
| LCS | G ▷ C52×C9×C31 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5^2,31,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^4,e^a=e^30,f^a=f^23489 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×C5⋊D45, C5⋊D5×D279, D9×C5⋊D155, … |
| maximal normal subgroup of | D31×C5⋊D45, C5⋊D5×D279, D9×C5⋊D155, … |
| maximal quotient of | C9⋊(C31⋊#1039), C2×C5⋊D1395 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13950, 88);