Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C11 ⋊ #1726 |
328 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 205 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=d,b^2=e,c^2=f,d^2=g,c^b=cg,h^c=h^10400 conjugacy classes — view the full character table.
| maximal subgroup of | #14640632, #14640634, #14644212, … |
| maximal normal subgroup of | #14640632, #14640634, #14644212, … |
| maximal quotient of | C8×#66879, C8×#66867, #14643128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4196);