Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| direct product | Dic15×C169 |
| unambiguous semidirect product | C3⋊(Dic5×C169) |
| derived, Hall | C3×C5 ⋊ C4×C169 |
| Hall | C3×C5×C169 ⋊ C4 |
| Hall | C5×C169 ⋊ Dic3 |
| Hall | C3×C169 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic3×C169 |
| Sylow | C3 ⋊ Dic5×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D15 |
| commutator, hypocenter | C3×C5 | C4×C169 |
| Frattini | C2×C13 | C13×D15 |
| Fitting | C2×C3×C5×C169 | C2 |
| socle, prime radical, cosocle | C2×C3×C5×C13 | C2×C13 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C169 | |
36 conjugacy classes of subgroups.
3042 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C169×Dic45, Dic15×C169⋊C3, C3×Dic15×C169, … |
| maximal normal subgroup of | Dic15×C169⋊C3, C3×Dic15×C169 |
| maximal quotient of | C169×Dic45, C3×Dic15×C169, C169×C3⋊Dic15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 11);