Finite Group DatabasebetaFinite Group Databasebeta| order | 22350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C149 · Schur multiplier (H2) = C5 |
| direct product | C149×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C5⋊D5×C149) |
| unambiguous semidirect product | C5⋊(D15×C149) |
| Fitting, socle, Hall | C3×C52×C149 ⋊ C2 |
| derived, Hall | C3×C52 ⋊ C2×C149 |
| Hall | C52×C149 ⋊ D3 |
| Hall | C3×C149 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D3×C149 |
| Sylow | C3 ⋊ C5⋊D5×C149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C149 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C149 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C149 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C149 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11175 |
5811 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22350, 25);