Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D25×#89204 |
| unambiguous semidirect product | C25⋊(C2×#89204) |
| derived, Hall | C72×C25 ⋊ C2×C9 |
| Hall | C25×#89204 ⋊ C2 |
| Hall | C72×D25 ⋊ C9 |
| Sylow | C72 ⋊ C9×D25 |
| Sylow | C25 ⋊ C2×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25×#3861 |
| commutator, hypocenter | C72×C25 | C2×C9 |
| Frattini | C3×C5 | D5×#3861 |
| Fitting, cosocle | C3×C72×C25 | C2×C3 |
| socle | C3×C5×C72 | C3×D5 |
| prime radical | C3×C72×D25 | C3 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C3 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11025 |
798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 78);