Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C49⋊#3874 |
| Fitting | C3×C52×C49 ⋊ D3 |
| derived | C49×C52⋊C3 ⋊ C2×C3 |
| Hall | C3×C49×C52⋊C3 ⋊ C2 |
| Hall | C52×C49 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ D49 |
| Sylow | C49 ⋊ C3×#3874 |
| Sylow | C52 ⋊ C3×D147 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C49⋊#3874 |
| commutator, cosocle, hypocenter | C49×C52⋊C3 | C2×C3 |
| Frattini | C7 | C3×C7⋊#3874 |
| Fitting | C3×C52×C49 | D3 |
| socle | C3×C52×C7 | D21 |
| LCS | G ▷ C49×C52⋊C3 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2205 |
831 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 108);