Finite Group DatabasebetaFinite Group Databasebeta| order | 31275 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×C52⋊(C139⋊C3) |
| unambiguous semidirect product | (C3×C52)⋊(C139⋊C3) |
| unambiguous semidirect product | (C3×C139)⋊(C52⋊C3) |
| Fitting, socle | C3×C52×C139 ⋊ C3 |
| derived, Hall | C52×C139 ⋊ C32 |
| Sylow | C139 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C52⋊(C139⋊C3) |
| commutator, cosocle, hypocenter | C52×C139 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C139 | C3 |
| LCS | G ▷ C52×C139 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6255 |
3483 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31275, 12);