Finite Group DatabasebetaFinite Group Databasebeta| order | 17622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3 |
| direct product | C2×C32×C89⋊C11 |
| unambiguous semidirect product | (C2×C89)⋊(C32×C11) |
| unambiguous semidirect product | (C2×C3×C89)⋊(C3×C11) |
| unambiguous semidirect product | (C2×C32×C89)⋊C11 |
| Fitting, socle, Hall | C2×C32×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C2×C32×C11 |
| Hall | C32×C89 ⋊ C2×C11 |
| Hall | C2×C89 ⋊ C32×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | C89⋊C11 |
| commutator, cosocle, hypocenter | C89 | C2×C32×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C2×C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1602 |
342 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic89⋊C11, C3×C3⋊(Dic89⋊C11), C3×Dic3×C89⋊C11, … |
| maximal normal subgroup of | C32×Dic89⋊C11, C3×C3⋊(Dic89⋊C11), C3×Dic3×C89⋊C11, … |
| maximal quotient of | C32×C4×C89⋊C11, C22×C32×C89⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17622, 19);