Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #1817 |
380 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 380 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 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | #14640304, #14640305, #14640313, … |
| maximal normal subgroup of | #14640304, #14640305, #14640313, … |
| maximal quotient of | #14647096, #14647099, #14647102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4578);