Finite Group DatabasebetaFinite Group Databasebeta| order | 17082 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#22555436 |
| derived, Hall | C13×C73 ⋊ C2×C9 |
| Hall | C2×C13×C73 ⋊ C9 |
| Hall | C2×C73 ⋊ C13⋊C9 |
| Sylow | C73 ⋊ C2×C13⋊C9 |
| Hall | C2×C13 ⋊ #10620321 |
| Sylow | C13 ⋊ C2×#10620321 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #15667865 |
| commutator, hypocenter | C13×C73 | C2×C9 |
| Frattini | C3 | C2×#15667865 |
| Fitting, socle, prime radical | C2×C3×C13×C73 | C3 |
| cosocle | C3×C13×C73 | C2×C3 |
| LCS | G ▷ C13×C73 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17082 |
1914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22555436, #46802650, #46802654, … |
| maximal normal subgroup of | C4×#22555436, #46802650, #46802654, … |
| maximal quotient of | C4×#22555436, C22×#22555436 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17082, 5);