Finite Group DatabasebetaFinite Group Databasebeta| order | 22530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D751⋊C5) |
| unambiguous semidirect product | (C751⋊C5)⋊D3 |
| unambiguous semidirect product | D2253⋊C5 |
| Fitting, socle, derived, Hall | C3×C751 ⋊ C2×C5 |
| Hall | C3×C751⋊C5 ⋊ C2 |
| Hall | D2253 ⋊ C5 |
| Hall | C751⋊C5 ⋊ D3 |
| Sylow | C751 ⋊ C5×D3 |
| Sylow | C3 ⋊ D751⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C751 | C2×C5 |
| LCS | G ▷ C3×C751 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2253 |
Polycyclic presentation:
2,3,5,751|b^a=b^2,d^a=d^750,d^c=d^80240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22530, 14);