Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D555 |
| unambiguous semidirect product | (C2×C3)⋊D555 |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊D111) |
| unambiguous semidirect product | (C2×C37)⋊(C3⋊D15) |
| Fitting, socle | C2×C32×C5×C37 ⋊ C2 |
| derived, Hall | C32×C5×C37 ⋊ C22 |
| Hall | C32×C37 ⋊ C2×D5 |
| Hall | C5×C37 ⋊ C2×C3⋊D3 |
| Hall | C32×C5 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C3⋊D15 |
| Sylow | C32 ⋊ C2×D185 |
| Sylow | C5 ⋊ C2×C3⋊D111 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D555 |
| commutator, hypocenter | C32×C5×C37 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C37 | C2 |
| LCS | G ▷ C32×C5×C37 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
1668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3⋊D2775, D5×C3⋊D555, C2×C5×C3⋊D555, … |
| maximal normal subgroup of | C2×C5×C3⋊D555 |
| maximal quotient of | C2×C3⋊D2775, D5×C3⋊D555, C2×C5×C3⋊D555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 171);