Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#135 ⋊ C2 |
| Sylow | C11 ⋊ #3045 |
504 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^10,f^c=fg172 conjugacy classes — view the full character table.
| maximal subgroup of | #14791814, #14791819, #14791829, … |
| maximal normal subgroup of | #14791814, #14791819, #14791829, … |
| maximal quotient of | #14739163, #14739174, #14739185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14047);