Finite Group DatabasebetaFinite Group Databasebeta| order | 31275 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C139 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C52⋊C3×C139 |
| unambiguous semidirect product | C52⋊(C32×C139) |
| unambiguous semidirect product | (C3×C52)⋊(C3×C139) |
| Fitting, socle | C3×C52×C139 ⋊ C3 |
| derived, Sylow | C52 ⋊ C32×C139 |
| Hall | C52×C139 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C139 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C32×C139 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C139 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C139 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6255 |
4587 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31275, 11);