Finite Group DatabasebetaFinite Group Databasebeta| order | 5796 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | D3×C7×D69 |
| unambiguous semidirect product | (C3×D3)⋊(C7×D23) |
| unambiguous semidirect product | (D3×C23)⋊(D3×C7) |
| Fitting, socle, Hall | C32×C7×C23 ⋊ C22 |
| derived, Hall | C32×C23 ⋊ C22×C7 |
| Hall | C7×C23 ⋊ D32 |
| Hall | C32×C7 ⋊ C2×D23 |
| Sylow | C23 ⋊ D32×C7 |
| Sylow | C32 ⋊ C2×C7×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×D69 |
| commutator, hypocenter | C32×C23 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C23 | C22 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
756 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×C7×D69, D3×C7×D345, C7×D15×D69, … |
| maximal normal subgroup of | C5×D3×C7×D69 |
| maximal quotient of | C5×D3×C7×D69, D3×C7×D345, C7×D15×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5796, 85);