Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic555 |
| derived, Hall | C32×C5×C37 ⋊ C4 |
| Hall | C32×C37 ⋊ Dic5 |
| Hall | C5×C37 ⋊ C3⋊Dic3 |
| Hall | C32×C5 ⋊ Dic37 |
| Sylow | C37 ⋊ C3⋊Dic15 |
| Sylow | C32 ⋊ Dic185 |
| Sylow | C5 ⋊ C3⋊Dic111 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D555 |
| commutator, hypocenter | C32×C5×C37 | C4 |
| Fitting, socle | C2×C32×C5×C37 | C2 |
| LCS | G ▷ C32×C5×C37 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,37,2|a^2=f,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^361668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊Dic2775, C3⋊(C3⋊#16814867), C5×C3⋊Dic555, … |
| maximal normal subgroup of | C5×C3⋊Dic555 |
| maximal quotient of | C3⋊Dic2775, C3⋊(C3⋊#16814867), C5×C3⋊Dic555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 76);