Finite Group DatabasebetaFinite Group Databasebeta| order | 25020 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C139⋊C3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C139⋊C3)⋊(C3×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C139⋊AGL(1,𝔽5))⋊C32 |
| unambiguous semidirect product | (C3×C139⋊AGL(1,𝔽5))⋊C3 |
| Fitting, socle | C3×C5×C139 ⋊ C3×C4 |
| derived, Hall | C5×C139 ⋊ C32×C4 |
| Hall | C3×C5×C139⋊C3 ⋊ C4 |
| Hall | C139⋊AGL(1,𝔽5) ⋊ C32 |
| Hall | C3×C139⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C139 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×(C139⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C139⋊C3)⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C139 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C139 | C3×C4 |
| prime radical | C3×D5×C139⋊C3 | C2 |
| cosocle | D5×C139 | C2×C32 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2085 |
321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25020, 62);