Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| Fitting, derived, Hall | C52×C49 ⋊ C2×C32 |
| Hall | C52⋊C3×C49⋊C3 ⋊ C2 |
| Hall | C52×D49 ⋊ C32 |
| Hall | D49 ⋊ C3×C52⋊C3 |
| Sylow | C49 ⋊ C2×C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C52×C49 | C2×C32 |
| Frattini | C7 | AGL(1,𝔽7)×C52⋊C3 |
| socle | C52×C7 | C3×AGL(1,𝔽7) |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 735 |
154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 100);