Finite Group DatabasebetaFinite Group Databasebeta| order | 31275 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C52×C139⋊C9 |
| unambiguous semidirect product | C139⋊(C52×C9) |
| unambiguous semidirect product | (C5×C139)⋊(C5×C9) |
| derived, Sylow | C139 ⋊ C52×C9 |
| Hall | C52×C139 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | C139⋊C3 |
| commutator, hypocenter | C139 | C52×C9 |
| Frattini | C3 | C52×C139⋊C3 |
| Fitting, socle, prime radical | C3×C52×C139 | C3 |
| cosocle | C3×C139 | C3×C52 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C3×C52 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31275 |
3675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31275, 8);