Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C37 · Schur multiplier (H2) = C3 |
| direct product | C32×AGL(1,𝔽5)×C37 |
| Fitting, socle, Hall | C32×C5×C37 ⋊ C4 |
| derived, Sylow | C5 ⋊ C32×C4×C37 |
| Hall | C5×C37 ⋊ C32×C4 |
| Hall | C32×C5 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C37 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C32×C4×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C37 | C4 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C32×C37 | |
72 conjugacy classes of subgroups.
1665 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C37×#1035, C32×C5×AGL(1,𝔽5)×C37, C32×C37×#1042, … |
| maximal normal subgroup of | C32×C5×AGL(1,𝔽5)×C37 |
| maximal quotient of | C32×C37×#1035, C32×C5×AGL(1,𝔽5)×C37, C32×C37×#1042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 118);