Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #2972 |
500 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 297 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,f^2=g,b^a=be,d^a=de,h^a=h^10,c^b=ce268 conjugacy classes — view the full character table.
| maximal subgroup of | #14647634, #14647637, #14647738, … |
| maximal normal subgroup of | #14647634, #14647637, #14647738, … |
| maximal quotient of | #14752446, #14752504, #14752662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13534);