Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#342 ⋊ C2 |
| Sylow | C11 ⋊ #2044 |
382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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|c^2=d,b^a=bd,c^a=ce,f^a=fg,h^a=h^10,c^b=cf,e^b=eg,h^b=h^10,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14666042, #14666044, #14666049, … |
| maximal normal subgroup of | #14666042, #14666044, #14666049, … |
| maximal quotient of | #14657044, #14657051, #14657058, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5762);