Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C5×C7 |
| direct product | C3×C72×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C3×C72×C5⋊D5) |
| unambiguous semidirect product | C5⋊(C3×C72×D15) |
| Fitting, socle, Hall | C32×C52×C72 ⋊ C2 |
| derived | C3×C52 ⋊ C2×C3×C72 |
| Hall | C52×C72 ⋊ C3×D3 |
| Hall | C32×C72 ⋊ C5⋊D5 |
| Hall | C32×C52 ⋊ C2×C72 |
| Sylow | C52 ⋊ C3×D3×C72 |
| Sylow | C32 ⋊ C72×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C72 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3×C72 | |
720 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7350 |
5733 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 511);