Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C37 · Schur multiplier (H2) = C1 |
| direct product | C9×AGL(1,𝔽5)×C37 |
| Fitting, Hall | C5×C9×C37 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C9×C37 |
| Hall | C5×C37 ⋊ C4×C9 |
| Hall | C5×C9 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C37 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C9×C37 |
| Frattini | C3 | C3×AGL(1,𝔽5)×C37 |
| Fitting | C5×C9×C37 | C4 |
| socle | C3×C5×C37 | C3×C4 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C9×C37 | |
36 conjugacy classes of subgroups.
1665 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C37×#1035, C5×C9×AGL(1,𝔽5)×C37, C9×C37×#1043, … |
| maximal normal subgroup of | C5×C9×AGL(1,𝔽5)×C37 |
| maximal quotient of | C9×C37×#1035, C5×C9×AGL(1,𝔽5)×C37, C9×C37×#1043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 25);