Finite Group DatabasebetaFinite Group Databasebeta| order | 5796 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D161⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C7×C23 ⋊ C22 |
| Hall | C32×C23 ⋊ C2×D7 |
| Hall | C7×C23 ⋊ C2×C3⋊D3 |
| Hall | C32×C7 ⋊ C2×D23 |
| Sylow | C23 ⋊ D7×C3⋊D3 |
| Sylow | C32 ⋊ D7×D23 |
| Sylow | C7 ⋊ C3⋊D3×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C23 | C22 |
| LCS | G ▷ C32×C7×C23 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,7,23|e^a=e^6,f^a=f^22,c^b=c^2,d^b=d^2,e^b=e^6393 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D161⋊(C3⋊D3), D161⋊(C3⋊D15), #44394654, … |
| maximal normal subgroup of | C5×D161⋊(C3⋊D3) |
| maximal quotient of | C5×D161⋊(C3⋊D3), D161⋊(C3⋊D15), #44394654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5796, 83);