Finite Group DatabasebetaFinite Group Databasebeta| order | 22050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C5×C7 |
| direct product | C72×C3⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | C3⋊(C72×(C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C3⋊(C5⋊D5))⋊(C3×C72) |
| Fitting, socle | C3×C52×C72 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C2×C3×C72 |
| Hall | C3×C72×C52⋊C3 ⋊ C2 |
| Hall | C52×C72 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C72 |
| Sylow | C52 ⋊ C3×D3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C3⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C72 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2205 |
1029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22050, 444);