Finite Group DatabasebetaFinite Group Databasebeta| order | 21825 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×C97⋊C9 |
| unambiguous semidirect product | C97⋊(C9×C25) |
| unambiguous semidirect product | (C25×C97)⋊C9 |
| derived, Sylow | C97 ⋊ C9×C25 |
| Hall | C25×C97 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C25 | C97⋊C3 |
| commutator, hypocenter | C97 | C9×C25 |
| Frattini | C3×C5 | C5×C97⋊C3 |
| Fitting | C3×C25×C97 | C3 |
| socle, prime radical, cosocle | C3×C5×C97 | C3×C5 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C25 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21825 |
2625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21825, 2);