Finite Group DatabasebetaFinite Group Databasebeta| order | 17545 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C11×C29 · Schur multiplier (H2) = C1 |
| direct product | C11×C29×C11⋊C5 |
| unambiguous semidirect product | C11⋊(C5×C11×C29) |
| unambiguous semidirect product | (C11×C29)⋊(C5×C11) |
| Fitting, socle, Hall | C112×C29 ⋊ C5 |
| derived | C11 ⋊ C5×C11×C29 |
| Sylow | C112 ⋊ C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C29 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C5×C11×C29 |
| Frattini | C1 | G |
| Fitting, socle | C112×C29 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C11×C29 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1595 |
2233 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C11⋊C5×D29, C11×C29×AGL(1,𝔽11), C11×C29⋊AGL(1,𝔽11), … |
| maximal normal subgroup of | C11×C11⋊C5×D29, C11×C29×AGL(1,𝔽11), C11×C29⋊AGL(1,𝔽11), … |
| maximal quotient of | C2×C11×C29×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17545, 5);