Finite Group DatabasebetaFinite Group Databasebeta| order | 8220 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic137 |
| derived, Sylow | C137 ⋊ C3×C4×C5 |
| Hall | C3×C5×C137 ⋊ C4 |
| Hall | C5×C137 ⋊ C3×C4 |
| Hall | C3×C137 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D137 |
| commutator, hypocenter | C137 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D137 |
| Fitting, socle | C2×C3×C5×C137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
2100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×Dic137, C3×C5×Dic411, C32×C5×Dic137 |
| maximal normal subgroup of | C5×C9×Dic137, C32×C5×Dic137 |
| maximal quotient of | C5×C9×Dic137, C3×C5×Dic411, C32×C5×Dic137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8220, 2);