Finite Group DatabasebetaFinite Group Databasebeta| order | 21900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1825 |
| derived, Hall | C25×C73 ⋊ C3×C4 |
| Hall | C3×C25×C73 ⋊ C4 |
| Hall | C3×C73 ⋊ Dic25 |
| Hall | C3×C25 ⋊ Dic73 |
| Sylow | C73 ⋊ C3×Dic25 |
| Sylow | C25 ⋊ C3×Dic73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1825 |
| commutator, hypocenter | C25×C73 | C3×C4 |
| Frattini | C2×C5 | C3×D365 |
| Fitting | C2×C3×C25×C73 | C2 |
| socle, prime radical | C2×C3×C5×C73 | D5 |
| cosocle | C2×C25×C73 | C2×C3 |
| LCS | G ▷ C25×C73 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21900 |
5484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21900, 5);