Finite Group DatabasebetaFinite Group Databasebeta| order | 22530 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D751⋊C3)⋊C5 |
| unambiguous semidirect product | (D751⋊C5)⋊C3 |
| unambiguous semidirect product | ((C751⋊C3)⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C751 ⋊ C2×C3×C5 |
| Hall | (C751⋊C3)⋊C5 ⋊ C2 |
| Hall | D751⋊C5 ⋊ C3 |
| Hall | D751⋊C3 ⋊ C5 |
| Hall | C751⋊C5 ⋊ C2×C3 |
| Hall | C751⋊C3 ⋊ C2×C5 |
| Hall | D751 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C751 | C2×C3×C5 |
| LCS | G ▷ C751 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 751 |
Polycyclic presentation:
2,3,5,751|d^a=d^750,d^b=d^678,d^c=d^8055 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22530, 18);