Finite Group DatabasebetaFinite Group Databasebeta| order | 21225 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C283⋊C3 |
| unambiguous semidirect product | C283⋊(C3×C25) |
| unambiguous semidirect product | (C25×C283)⋊C3 |
| Fitting, Hall | C25×C283 ⋊ C3 |
| derived, Sylow | C283 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | C283⋊C3 |
| commutator, hypocenter | C283 | C3×C25 |
| Frattini | C5 | C5×C283⋊C3 |
| Fitting | C25×C283 | C3 |
| socle, cosocle | C5×C283 | C3×C5 |
| prime radical | C5×C283⋊C3 | C5 |
| LCS | G ▷ C283 | |
| UCS | C1 ◁ C25 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7075 |
2425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21225, 2);