Finite Group DatabasebetaFinite Group Databasebeta| order | 21450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D275 |
| unambiguous semidirect product | C11⋊(C13⋊C3×D25) |
| unambiguous semidirect product | C25⋊(D11×C13⋊C3) |
| unambiguous semidirect product | (C13×D275)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C13×C25 | C2×C3 |
| Frattini | C5 | C13⋊C3×D55 |
| socle | C5×C11×C13 | C3×D5 |
| LCS | G ▷ C11×C13×C25 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3575 |
973 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21450, 32);