Finite Group DatabasebetaFinite Group Databasebeta| order | 25020 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊(D139⋊C3) |
| unambiguous semidirect product | (C3⋊(D139⋊C3))⋊D5 |
| unambiguous semidirect product | (C5⋊(D139⋊C3))⋊D3 |
| unambiguous semidirect product | (D15⋊D139)⋊C3 |
| Fitting, socle, derived | C3×C5×C139 ⋊ C22×C3 |
| Hall | C3×C5×C139⋊C3 ⋊ C22 |
| Hall | C3×C139⋊C3 ⋊ C2×D5 |
| Hall | C5×C139 ⋊ C2×C3×D3 |
| Sylow | C139 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ D3×D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C139 | C22×C3 |
| LCS | G ▷ C3×C5×C139 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2085 |
Polycyclic presentation:
2^2,3^2,5,139|e^a=e^4,f^a=f^138,d^b=d^2,e^b=e^4,f^c=f^42243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25020, 71);