Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10620321⋊D13 |
| derived, Hall | C13×C73 ⋊ C2×C9 |
| Hall | C13×#10620321 ⋊ C2 |
| Hall | D949 ⋊ C9 |
| Hall | #10620321 ⋊ D13 |
| Sylow | C73 ⋊ C9×D13 |
| Sylow | C13 ⋊ #10620321⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C73⋊C3)⋊D13 |
| commutator, hypocenter | C13×C73 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C73 | C2×C3 |
| prime radical | C3×D949 | C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8541 |
Polycyclic presentation:
2,3,13,73,3|b^3=e,c^a=c^12,d^a=d^72,d^b=d^8540 conjugacy classes — view the full character table.
| maximal subgroup of | #46802679, #46802680, D13×#10620321⋊C2, … |
| maximal normal subgroup of | #46802679, #46802680, D13×#10620321⋊C2, … |
| maximal quotient of | #46802655, C2×#10620321⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 21);