Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #1799 |
380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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=d,b^a=bd,c^a=ce,e^a=eg,h^a=h^10,f^c=fg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14640861, #14640862, #14640863, … |
| maximal normal subgroup of | #14640861, #14640862, #14640863, … |
| maximal quotient of | #14646430, #14646434, #14646438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4498);