Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of #4314 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#4314 |
| Fitting | C82×C11 ⋊ C2 |
| Sylow | C11 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14665538, C16×#4314, #14665545, … |
| maximal normal subgroup of | #14665538, C16×#4314, #14665545, … |
| maximal quotient of | C8×#66885, C8×#66880, C8×#66881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 3312);