Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×C22⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ #3187 |
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^10,c^b=ce,f^c=fg,h^c=h^10232 conjugacy classes — view the full character table.
| maximal subgroup of | #14650331, #14650333, #14650352, … |
| maximal normal subgroup of | #14650331, #14650333, #14650352, … |
| maximal quotient of | #14762779, #14762786, #14764034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 15268);