Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #1749 |
412 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 165 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,c^b=cg,h^b=h^10376 conjugacy classes — view the full character table.
| maximal subgroup of | #14640312, #14640313, #14640345, … |
| maximal normal subgroup of | #14640312, #14640313, #14640345, … |
| maximal quotient of | #14644246, #14644256, #14644283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4272);