Finite Group DatabasebetaFinite Group Databasebeta| order | 8220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C137 · Schur multiplier (H2) = C2 |
| direct product | D3×D5×C137 |
| unambiguous semidirect product | (C5×D3)⋊(C2×C137) |
| unambiguous semidirect product | (C3×D5)⋊(C2×C137) |
| unambiguous semidirect product | D15⋊(C2×C137) |
| Fitting, socle, Hall | C3×C5×C137 ⋊ C22 |
| derived, Hall | C3×C5 ⋊ C22×C137 |
| Hall | C5×C137 ⋊ C2×D3 |
| Hall | C3×C137 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D3×C137 |
| Sylow | C3 ⋊ C2×D5×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C137 | D3×D5 |
| commutator, hypocenter | C3×C5 | C22×C137 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C137 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C137 | |
40 conjugacy classes of subgroups.
1644 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D9×C137, C3×D3×D5×C137, D3×D15×C137, … |
| maximal normal subgroup of | C3×D3×D5×C137 |
| maximal quotient of | D5×D9×C137, C3×D3×D5×C137, D3×D15×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8220, 25);