Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| direct product | C3×C3⋊(C7⋊D175) |
| unambiguous semidirect product | C3⋊(C3×C7⋊D175) |
| unambiguous semidirect product | C25⋊(C3×C3⋊(C7⋊D7)) |
| Fitting, Hall | C32×C72×C25 ⋊ C2 |
| derived | C3×C72×C25 ⋊ C2×C3 |
| Hall | C72×C25 ⋊ C3×D3 |
| Hall | C32×C72 ⋊ D25 |
| Hall | C32×C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C3×D75 |
| Sylow | C25 ⋊ C3×C3⋊(C7⋊D7) |
| Sylow | C32 ⋊ C7⋊D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C7⋊D175) |
| commutator, cosocle, hypocenter | C3×C72×C25 | C2×C3 |
| Frattini | C5 | C3×C3⋊(C5⋊(C7⋊D7)) |
| Fitting | C32×C72×C25 | C2 |
| socle | C32×C5×C72 | D5 |
| LCS | G ▷ C3×C72×C25 | |
| UCS | C1 ◁ C3 | |
270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7350 |
5517 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 214);