Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D735 |
| unambiguous semidirect product | C3⋊(C5×D735) |
| unambiguous semidirect product | C5⋊(C5×C3⋊D147) |
| unambiguous semidirect product | C49⋊(C5×C3⋊D15) |
| Fitting, Hall | C32×C52×C49 ⋊ C2 |
| derived | C32×C5×C49 ⋊ C2×C5 |
| Hall | C52×C49 ⋊ C3⋊D3 |
| Hall | C32×C49 ⋊ C5×D5 |
| Hall | C32×C52 ⋊ D49 |
| Sylow | C49 ⋊ C5×C3⋊D15 |
| Sylow | C52 ⋊ C3⋊D147 |
| Sylow | C32 ⋊ C5×D245 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D735 |
| commutator, cosocle, hypocenter | C32×C5×C49 | C2×C5 |
| Frattini | C7 | C5×C3⋊D105 |
| Fitting | C32×C52×C49 | C2 |
| socle | C32×C52×C7 | D7 |
| LCS | G ▷ C32×C5×C49 | |
| UCS | C1 ◁ C5 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4410 |
5520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 148);