Finite Group DatabasebetaFinite Group Databasebeta| order | 17105 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C311⋊C5 |
| unambiguous semidirect product | C311⋊(C5×C11) |
| Fitting, socle, Hall | C11×C311 ⋊ C5 |
| derived, Sylow | C311 ⋊ C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C311⋊C5 |
| commutator, cosocle, hypocenter | C311 | C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C311 | C5 |
| LCS | G ▷ C311 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3421 |
737 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C311⋊C5, C11×D311⋊C5, D11×C311⋊C5, … |
| maximal normal subgroup of | C2×C11×C311⋊C5, C11×D311⋊C5, D11×C311⋊C5, … |
| maximal quotient of | C2×C11×C311⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17105, 2);