Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| isoclinism | isoclinic class of Dic22 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#66876 |
| Sylow | C11 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14640604, #14640605, #14640606, … |
| maximal normal subgroup of | #14640604, #14640605, #14640606, … |
| maximal quotient of | C8×#66876, #14662766, #14662795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6104);