Finite Group DatabasebetaFinite Group Databasebeta| order | 25270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C361 · Schur multiplier (H2) = C1 |
| direct product | D35×C361 |
| unambiguous semidirect product | C5⋊(D7×C361) |
| unambiguous semidirect product | C7⋊(D5×C361) |
| Fitting, Hall | C5×C7×C361 ⋊ C2 |
| derived, Hall | C5×C7 ⋊ C2×C361 |
| Hall | C7×C361 ⋊ D5 |
| Hall | C5×C361 ⋊ D7 |
| Sylow | C7 ⋊ D5×C361 |
| Sylow | C5 ⋊ D7×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C361 | D35 |
| commutator, hypocenter | C5×C7 | C2×C361 |
| Frattini | C19 | C19×D35 |
| Fitting | C5×C7×C361 | C2 |
| socle, cosocle | C5×C7×C19 | C2×C19 |
| prime radical | C19×D35 | C19 |
| LCS | G ▷ C5×C7 | |
| UCS | C1 ◁ C361 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12635 |
6859 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25270, 7);