Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C11×#497 ⋊ C2 |
| Sylow | C11 ⋊ #3153 |
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 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|b^2=e,c^2=fg,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^10,h^d=h^10112 conjugacy classes — view the full character table.
| maximal subgroup of | #14674065, #14734990, #14734998, … |
| maximal normal subgroup of | #14674065, #14734990, #14734998, … |
| maximal quotient of | #14741633, #14741648, #14741677, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14973);