Finite Group DatabasebetaFinite Group Databasebeta| order | 31275 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C52⋊(C139⋊C9) |
| unambiguous semidirect product | C139⋊(C52⋊C9) |
| derived, Hall | C52×C139 ⋊ C9 |
| Sylow | C139 ⋊ C52⋊C9 |
| Sylow | C52 ⋊ C139⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C52⋊(C139⋊C3) |
| commutator, hypocenter | C52×C139 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C52×C139 | C3 |
| LCS | G ▷ C52×C139 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6255 |
Polycyclic presentation:
3,5^2,139,3|a^3=e,b^a=b^2c^3,c^a=bc^2,d^a=d^423483 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31275, 6);