Finite Group DatabasebetaFinite Group Databasebeta| order | 17182 |
| isoclinism | isoclinic class of D121 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D121 |
| unambiguous semidirect product | C121⋊(C2×C71) |
| Fitting, Hall | C71×C121 ⋊ C2 |
| derived, Sylow | C121 ⋊ C2×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D121 |
| commutator, cosocle, hypocenter | C121 | C2×C71 |
| Frattini | C11 | D11×C71 |
| Fitting | C71×C121 | C2 |
| socle | C11×C71 | D11 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C71 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8591 |
4402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D71×D121, C2×C71×D121 |
| maximal normal subgroup of | D71×D121, C2×C71×D121 |
| maximal quotient of | C71×Dic121, C2×C71×D121 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17182, 2);