Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×C8×D11 |
| Fitting | C2×C4×C8×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C22×C4×C8 |
760 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
448 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×#1273, #14643153, #14643157, … |
| maximal normal subgroup of | D11×#1273, #14643153, #14643157, … |
| maximal quotient of | C2×C82×D11, C2×D11×#322, C8×M16×D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12909);