Finite Group DatabasebetaFinite Group Databasebeta| order | 10020 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic501 |
| unambiguous semidirect product | C3⋊(C5×Dic167) |
| unambiguous semidirect product | C167⋊(C5×Dic3) |
| derived, Hall | C3×C167 ⋊ C4×C5 |
| Hall | C3×C5×C167 ⋊ C4 |
| Hall | C5×C167 ⋊ Dic3 |
| Sylow | C167 ⋊ C5×Dic3 |
| Hall | C3×C5 ⋊ Dic167 |
| Sylow | C3 ⋊ C5×Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D501 |
| commutator, hypocenter | C3×C167 | C4×C5 |
| Frattini | C2 | C5×D501 |
| Fitting, socle, prime radical | C2×C3×C5×C167 | C2 |
| cosocle | C2×C3×C167 | C2×C5 |
| LCS | G ▷ C3×C167 | |
| UCS | C1 ◁ C2×C5 | |
24 conjugacy classes of subgroups.
2520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic1503, C5×C3⋊Dic501, C3×C5×Dic501 |
| maximal normal subgroup of | C3×C5×Dic501 |
| maximal quotient of | C5×Dic1503, C5×C3⋊Dic501, C3×C5×Dic501 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10020, 6);