Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #1885 |
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=df,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,d^b=dg,e^b=eg,f^b=fg,h^b=h^10,d^c=dg,f^c=fg142 conjugacy classes — view the full character table.
| maximal subgroup of | #14669583, #14669586, #14669597, … |
| maximal normal subgroup of | #14669583, #14669586, #14669597, … |
| maximal quotient of | #14648416, #14648436, #14648686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4896);