Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(#261⋊C9) |
| unambiguous semidirect product | (C23⋊#261)⋊C9 |
| derived, Hall | C13×C23 ⋊ C4×C9 |
| Hall | C23×C13⋊C9 ⋊ C4 |
| Hall | C23⋊#261 ⋊ C9 |
| Hall | C13⋊C9 ⋊ Dic23 |
| Sylow | C23 ⋊ #261⋊C9 |
| Sylow | C13 ⋊ C9×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C23⋊AGL(1,𝔽13) |
| commutator, hypocenter | C13×C23 | C4×C9 |
| Fitting, socle | C3×C13×C23 | C3×C4 |
| prime radical, cosocle | C3×C23×D13 | C2×C3 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,13,23,3|a^2=c,b^3=f,d^a=d^5,e^a=e^22,d^b=d^3,d^c=d^12303 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 15);