Finite Group DatabasebetaFinite Group Databasebeta| order | 4030 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D403 |
| unambiguous semidirect product | C13⋊(C5×D31) |
| Fitting, socle, Hall | C5×C13×C31 ⋊ C2 |
| derived, Hall | C13×C31 ⋊ C2×C5 |
| Hall | C5×C31 ⋊ D13 |
| Hall | C5×C13 ⋊ D31 |
| Sylow | C31 ⋊ C5×D13 |
| Sylow | C13 ⋊ C5×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D403 |
| commutator, cosocle, hypocenter | C13×C31 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C31 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2015 |
1015 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D403, C5×D1209, C5×(C31⋊C3)⋊D13, … |
| maximal normal subgroup of | C3×C5×D403, C5×(C31⋊C3)⋊D13, C5×(C13⋊C3)⋊D31, … |
| maximal quotient of | C3×C5×D403, C5×D1209, C25×D403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4030, 5);