Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1839 |
240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^c=h^10256 conjugacy classes — view the full character table.
| maximal subgroup of | #14641792, #14641794, #14641797, … |
| maximal normal subgroup of | #14641792, #14641794, #14641797, … |
| maximal quotient of | #14647490, #14647491, #14647492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4652);