Finite Group DatabasebetaFinite Group Databasebeta| order | 25020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | Dic5×C139⋊C9 |
| unambiguous semidirect product | (Dic5×C139)⋊C9 |
| derived, Hall | C5×C139 ⋊ C4×C9 |
| Hall | C5×C139⋊C9 ⋊ C4 |
| Hall | Dic5×C139 ⋊ C9 |
| Sylow | C139 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ C4×C139⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D5×C139⋊C3 |
| commutator, hypocenter | C5×C139 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C139 | C2×C3 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25020 |
1176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25020, 11);