Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×C22⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ #2973 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14647742, #14647745, #14648465, … |
| maximal normal subgroup of | #14647742, #14647745, #14648465, … |
| maximal quotient of | #14752448, #14752462, #14752506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13536);