Finite Group DatabasebetaFinite Group Databasebeta| order | 4020 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic335 |
| derived, Hall | C5×C67 ⋊ C3×C4 |
| Hall | C3×C5×C67 ⋊ C4 |
| Hall | C3×C67 ⋊ Dic5 |
| Sylow | C67 ⋊ C3×Dic5 |
| Hall | C3×C5 ⋊ Dic67 |
| Sylow | C5 ⋊ C3×Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D335 |
| commutator, hypocenter | C5×C67 | C3×C4 |
| Frattini | C2 | C3×D335 |
| Fitting, socle, prime radical | C2×C3×C5×C67 | C2 |
| cosocle | C2×C5×C67 | C2×C3 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 4020 |
1014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic335, (C67⋊C9)⋊Dic5, C3×(C67⋊C3)⋊Dic5, … |
| maximal normal subgroup of | C9×Dic335, (C67⋊C9)⋊Dic5, C3×(C67⋊C3)⋊Dic5, … |
| maximal quotient of | C9×Dic335, C32×Dic335, C3×Dic1005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4020, 5);