Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10620323⋊D13 |
| Fitting, socle, derived, Hall | C13×C73 ⋊ C2×C9 |
| Hall | C13×#10620323 ⋊ C2 |
| Hall | D949 ⋊ C9 |
| Hall | #10620323 ⋊ D13 |
| Sylow | C73 ⋊ C9×D13 |
| Sylow | C13 ⋊ #10620323⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C73 | C2×C9 |
| prime radical | (C73⋊C3)⋊D13 | C3 |
| cosocle | C13×C73⋊C3 | C2×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 949 |
Polycyclic presentation:
2,3^2,13,73|b^3=c,d^a=d^12,e^a=e^72,e^b=e^2,e^c=e^8124 conjugacy classes — view the full character table.
| maximal subgroup of | #46802815, #46802816, D13×#10620323⋊C2, … |
| maximal normal subgroup of | #46802815, #46802816, D13×#10620323⋊C2, … |
| maximal quotient of | #46802746, C2×#10620323⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 36);