Finite Group DatabasebetaFinite Group Databasebeta| order | 5082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C7⋊(C11⋊D11)) |
| unambiguous semidirect product | C7⋊(C3⋊(C11⋊D11)) |
| unambiguous semidirect product | C11⋊D231 |
| Fitting, socle, derived, Hall | C3×C7×C112 ⋊ C2 |
| Hall | C7×C112 ⋊ D3 |
| Hall | C3×C112 ⋊ D7 |
| Sylow | C112 ⋊ D21 |
| Hall | C3×C7 ⋊ C11⋊D11 |
| Sylow | C7 ⋊ C3⋊(C11⋊D11) |
| Sylow | C3 ⋊ C7⋊(C11⋊D11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C112 | C2 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11^2|b^a=b^2,c^a=c^6,d^a=d^10,e^a=e^101272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5082, 40);