Finite Group DatabasebetaFinite Group Databasebeta| order | 17457 |
| isoclinism | isoclinic class of C23⋊C11 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×C23⋊C11 |
| unambiguous semidirect product | C23⋊(C3×C11×C23) |
| unambiguous semidirect product | (C3×C23)⋊(C11×C23) |
| Fitting, socle, Hall | C3×C232 ⋊ C11 |
| derived | C23 ⋊ C3×C11×C23 |
| Sylow | C232 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C3×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
897 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C23×AGL(1,𝔽23), C3×(C23⋊C11)⋊D23, C3×D23×C23⋊C11, … |
| maximal normal subgroup of | C3×C23×AGL(1,𝔽23), C3×(C23⋊C11)⋊D23, C3×D23×C23⋊C11, … |
| maximal quotient of | C2×C3×C23×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17457, 6);