Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#382 ⋊ C2 |
| Sylow | C11 ⋊ #2073 |
258 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 79 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=eg,c^2=d,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^10,f^c=fg172 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2073, C2×#13070030, #14782527, … |
| maximal normal subgroup of | D11×#2073, C2×#13070030, #14782527, … |
| maximal quotient of | #14658508, #14658513, #14658528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5924);