Finite Group DatabasebetaFinite Group Databasebeta| order | 21525 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C25 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C41⋊C25 |
| unambiguous semidirect product | C41⋊(C3×C7×C25) |
| unambiguous semidirect product | (C3×C41)⋊(C7×C25) |
| unambiguous semidirect product | (C3×C7×C41)⋊C25 |
| derived, Sylow | C41 ⋊ C3×C7×C25 |
| Hall | C3×C7×C41 ⋊ C25 |
| Hall | C7×C41 ⋊ C3×C25 |
| Hall | C3×C41 ⋊ C7×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C7 | C41⋊C5 |
| commutator, hypocenter | C41 | C3×C7×C25 |
| Frattini | C5 | C3×C7×C41⋊C5 |
| Fitting, socle, prime radical | C3×C5×C7×C41 | C5 |
| cosocle | C5×C41 | C3×C5×C7 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C5×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21525 |
1365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21525, 2);