Finite Group DatabasebetaFinite Group Databasebeta| order | 17457 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×#19154122 |
| Fitting, socle, Hall | C3×C232 ⋊ C11 |
| derived, Sylow | C232 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19154122 |
| commutator, cosocle, hypocenter | C232 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C11 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#26042789, C3×#26042795, C3×#26042796, … |
| maximal normal subgroup of | C3×#26042789, C3×#26042795, C3×#26042796, … |
| maximal quotient of | C2×C3×#19154122 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17457, 9);