Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#10622199 |
| Sylow | C11 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10622199, Dic11×#350, #14668826, … |
| maximal normal subgroup of | C4×#10622199, Dic11×#350, #14668826, … |
| maximal quotient of | C2×#13066542, #14662848, C2×#13066558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6134);