Finite Group DatabasebetaFinite Group Databasebeta| order | 6060 |
| automorphism | Aut(G) order 2424000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3030 |
| direct product | C2×D1515 |
| unambiguous semidirect product | (C2×C3)⋊D505 |
| unambiguous semidirect product | (C2×C5)⋊D303 |
| unambiguous semidirect product | (C2×C101)⋊D15 |
| Fitting, socle | C2×C3×C5×C101 ⋊ C2 |
| derived, Hall | C3×C5×C101 ⋊ C22 |
| Hall | C5×C101 ⋊ C2×D3 |
| Hall | C3×C101 ⋊ C2×D5 |
| Sylow | C101 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D101 |
| Sylow | C5 ⋊ C2×D303 |
| Sylow | C3 ⋊ C2×D505 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1515 |
| commutator, hypocenter | C3×C5×C101 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C101 | C2 |
| LCS | G ▷ C3×C5×C101 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
1518 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4545, D3×D1515, C2×C3⋊D1515, … |
| maximal normal subgroup of | C2×C3×D1515, C2×C3⋊(C5⋊(D101⋊C5)), C2×C5×D1515, … |
| maximal quotient of | C2×D4545, D3×D1515, C2×C3⋊D1515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6060, 42);