Finite Group DatabasebetaFinite Group Databasebeta| order | 21645 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×#16864525 |
| derived, Hall | C13×C37 ⋊ C5×C9 |
| Hall | C5×C13×C37 ⋊ C9 |
| Hall | C5×C37 ⋊ C13⋊C9 |
| Hall | C5×C13 ⋊ #66524 |
| Sylow | C37 ⋊ C5×C13⋊C9 |
| Sylow | C13 ⋊ C5×#66524 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | #13089649 |
| commutator, hypocenter | C13×C37 | C5×C9 |
| Frattini | C3 | C5×#13089649 |
| Fitting, socle, prime radical | C3×C5×C13×C37 | C3 |
| cosocle | C3×C13×C37 | C3×C5 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21645 |
2445 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21645, 5);