Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D299⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C13×C23 ⋊ C22 |
| Hall | C13×C23 ⋊ C2×C3⋊D3 |
| Hall | C32×C23 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×D23 |
| Sylow | C23 ⋊ C3⋊D3×D13 |
| Sylow | C13 ⋊ C3⋊D3×D23 |
| Sylow | C32 ⋊ D13×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C23 | C22 |
| LCS | G ▷ C32×C13×C23 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,13,23|e^a=e^12,f^a=f^22,c^b=c^2,d^b=d^2,e^b=e^12708 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 99);