Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#22555440 |
| Fitting, socle, Hall | C2×C13×C73 ⋊ C9 |
| derived, Hall | C13×C73 ⋊ C2×C9 |
| Hall | C2×C73 ⋊ C13⋊C9 |
| Sylow | C73 ⋊ C2×C13⋊C9 |
| Hall | C2×C13 ⋊ #10620323 |
| Sylow | C13 ⋊ C2×#10620323 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22555440 |
| commutator, hypocenter | C13×C73 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C73 | C9 |
| prime radical | C2×C13×C73⋊C3 | C3 |
| cosocle | C13×C73⋊C3 | C2×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1898 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #46802738, #46802740, #46802744, … |
| maximal normal subgroup of | #46802738, #46802740, #46802744, … |
| maximal quotient of | C4×#22555440, C22×#22555440 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 40);