Finite Group DatabasebetaFinite Group Databasebeta| order | 6660 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C37 · Schur multiplier (H2) = C3 |
| direct product | C5×#157×C37 |
| Fitting, socle, Hall | C32×C5×C37 ⋊ C4 |
| derived, Sylow | C32 ⋊ C4×C5×C37 |
| Hall | C32×C37 ⋊ C4×C5 |
| Hall | C32×C5 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C37 | #157 |
| commutator, hypocenter | C32 | C4×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C37 | C4 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C37 | |
40 conjugacy classes of subgroups.
1110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×#157×C37, C52×#157×C37, C5×C37×#4379, … |
| maximal normal subgroup of | C25×#157×C37, C52×#157×C37 |
| maximal quotient of | C25×#157×C37, C52×#157×C37, C5×C37×#4379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6660, 158);