Finite Group DatabasebetaFinite Group Databasebeta| order | 17262 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D137 |
| unambiguous semidirect product | C137⋊(C2×C7⋊C9) |
| unambiguous semidirect product | (C7×D137)⋊C9 |
| derived, Hall | C7×C137 ⋊ C2×C9 |
| Hall | C7⋊C9×C137 ⋊ C2 |
| Hall | C7×D137 ⋊ C9 |
| Sylow | C137 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ C9×D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D137 |
| commutator, hypocenter | C7×C137 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C137 | C2×C3 |
| prime radical | C3×C7×D137 | C3 |
| LCS | G ▷ C7×C137 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8631 |
1050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C7⋊C9)⋊#10587739, D7⋊C9×D137, C7⋊C9×#10587739, … |
| maximal normal subgroup of | (C7⋊C9)⋊#10587739, D7⋊C9×D137, C7⋊C9×#10587739, … |
| maximal quotient of | C7⋊C9×Dic137, C2×C7⋊C9×D137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17262, 10);