Finite Group DatabasebetaFinite Group Databasebeta| order | 16874 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C13×D59 |
| unambiguous semidirect product | C59⋊(C2×C11×C13) |
| Fitting, socle, Hall | C11×C13×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C11×C13 |
| Hall | C13×C59 ⋊ C2×C11 |
| Hall | C11×C59 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C13 | D59 |
| commutator, cosocle, hypocenter | C59 | C2×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C59 | C2 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C11×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8437 |
4433 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D13×D59, C13×D11×D59, D59×D143, … |
| maximal normal subgroup of | C11×D13×D59, C13×D11×D59, D59×D143, … |
| maximal quotient of | C11×C13×Dic59, C2×C11×C13×D59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16874, 2);