Finite Group DatabasebetaFinite Group Databasebeta| order | 10660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | #261×C41⋊C5 |
| unambiguous semidirect product | (C41×#261)⋊C5 |
| Fitting, socle, derived, Hall | C13×C41 ⋊ C4×C5 |
| Hall | C13×C41⋊C5 ⋊ C4 |
| Hall | C41×#261 ⋊ C5 |
| Sylow | C41 ⋊ C5×#261 |
| Sylow | C13 ⋊ C4×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C41 | C4×C5 |
| prime radical | D13×C41⋊C5 | C2 |
| cosocle | D13×C41 | C2×C5 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
91 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×C41⋊C5, C3×#261×C41⋊C5, C3⋊#261×C41⋊C5 |
| maximal normal subgroup of | AGL(1,𝔽13)×C41⋊C5, C3×#261×C41⋊C5 |
| maximal quotient of | C3×#261×C41⋊C5, C3⋊#261×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10660, 18);