Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊(D13⋊C3) |
| unambiguous semidirect product | (C3⋊(D13⋊C3))⋊D23 |
| unambiguous semidirect product | (C23⋊(D13⋊C3))⋊D3 |
| unambiguous semidirect product | (D39⋊D23)⋊C3 |
| Fitting, socle, derived | C3×C13×C23 ⋊ C22×C3 |
| Hall | C3×C23×C13⋊C3 ⋊ C22 |
| Hall | C13×C23 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×D23 |
| Sylow | C23 ⋊ D3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D3×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C23 | C22×C3 |
| LCS | G ▷ C3×C13×C23 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,13,23|e^a=e^12,f^a=f^22,d^b=d^2,e^b=e^12,e^c=e^3189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 71);