Finite Group DatabasebetaFinite Group Databasebeta| order | 7860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×D131 |
| Fitting, socle, Hall | C3×C5×C131 ⋊ C22 |
| derived, Hall | C3×C131 ⋊ C22×C5 |
| Hall | C5×C131 ⋊ C2×D3 |
| Sylow | C131 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D131 |
| Sylow | C3 ⋊ C2×C5×D131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×D131 |
| commutator, hypocenter | C3×C131 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C131 | C22 |
| LCS | G ▷ C3×C131 | |
| UCS | C1 ◁ C5 | |
40 conjugacy classes of subgroups.
1005 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D9×D131, C3×C5×D3×D131, C5×D3×D393, … |
| maximal normal subgroup of | C3×C5×D3×D131 |
| maximal quotient of | C5×D9×D131, C3×C5×D3×D131, C5×D3×D393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7860, 23);