Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #1467 |
236 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 236 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) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=f,c^2=fg,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^10,e^b=ef232 conjugacy classes — view the full character table.
| maximal subgroup of | #14640888, #14640889, #14641087, … |
| maximal normal subgroup of | #14640888, #14640889, #14641087, … |
| maximal quotient of | #14641966, #14641979, #14641992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2854);