Finite Group DatabasebetaFinite Group Databasebeta| order | 24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((D271⋊C3)⋊C5) |
| unambiguous semidirect product | ((C271⋊C3)⋊C5)⋊D3 |
| unambiguous semidirect product | (C3⋊(D271⋊C3))⋊C5 |
| unambiguous semidirect product | (C3⋊(D271⋊C5))⋊C3 |
| Fitting, socle, derived | C3×C271 ⋊ C2×C3×C5 |
| Hall | C3×(C271⋊C3)⋊C5 ⋊ C2 |
| Hall | C3⋊(D271⋊C3) ⋊ C5 |
| Hall | C3×C271⋊C3 ⋊ C2×C5 |
| Hall | C271⋊C5 ⋊ C3×D3 |
| Sylow | C271 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C271 | C2×C3×C5 |
| LCS | G ▷ C3×C271 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 813 |
Polycyclic presentation:
2,3,5,3,271|d^a=d^2,e^a=e^270,e^b=e^28,e^c=e^1072 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24390, 23);