Finite Group DatabasebetaFinite Group Databasebeta| order | 16005 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C97 · Schur multiplier (H2) = C1 |
| direct product | C3×C11⋊C5×C97 |
| unambiguous semidirect product | C11⋊(C3×C5×C97) |
| unambiguous semidirect product | (C3×C11)⋊(C5×C97) |
| unambiguous semidirect product | (C3×C11×C97)⋊C5 |
| Fitting, socle, Hall | C3×C11×C97 ⋊ C5 |
| derived, Sylow | C11 ⋊ C3×C5×C97 |
| Hall | C11×C97 ⋊ C3×C5 |
| Hall | C3×C11 ⋊ C5×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C97 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C3×C5×C97 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C97 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C97 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3201 |
2037 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C11⋊C5×C97, C3×C11⋊C5×D97, C3×C97×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×C3×C11⋊C5×C97, C3×C11⋊C5×D97, C3×C97×AGL(1,𝔽11), … |
| maximal quotient of | C2×C3×C11⋊C5×C97 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16005, 2);