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 | C8×#4318 |
| Sylow | C11 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #14640663, #14640664, #14640669, … |
| maximal normal subgroup of | #14640663, #14640664, #14640669, … |
| maximal quotient of | C8×#66867, #14643155, #14644199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2790);