Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16809980 |
| Fitting, Hall | C3×C5×C169 ⋊ C4 |
| derived, Hall | C5×C169 ⋊ C3×C4 |
| Hall | C3×C169 ⋊ AGL(1,𝔽5) |
| Sylow | C169 ⋊ C3×AGL(1,𝔽5) |
| Hall | C3×C5 ⋊ #10621721 |
| Sylow | C5 ⋊ C3×#10621721 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16809980 |
| commutator, hypocenter | C5×C169 | C3×C4 |
| Frattini | C13 | C3×#63121 |
| Fitting | C3×C5×C169 | C4 |
| socle | C3×C5×C13 | #261 |
| prime radical | C3×D845 | C2 |
| cosocle | D845 | C2×C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
645 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 27);