Finite Group DatabasebetaFinite Group Databasebeta| order | 10020 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic835 |
| unambiguous semidirect product | C167⋊(C3×Dic5) |
| derived, Hall | C5×C167 ⋊ C3×C4 |
| Hall | C3×C5×C167 ⋊ C4 |
| Hall | C3×C167 ⋊ Dic5 |
| Sylow | C167 ⋊ C3×Dic5 |
| Hall | C3×C5 ⋊ Dic167 |
| Sylow | C5 ⋊ C3×Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D835 |
| commutator, hypocenter | C5×C167 | C3×C4 |
| Frattini | C2 | C3×D835 |
| Fitting, socle, prime radical | C2×C3×C5×C167 | C2 |
| cosocle | C2×C5×C167 | C2×C3 |
| LCS | G ▷ C5×C167 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
2514 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic835, C3×Dic2505, C32×Dic835 |
| maximal normal subgroup of | C9×Dic835, C32×Dic835 |
| maximal quotient of | C9×Dic835, C3×Dic2505, C32×Dic835 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10020, 4);