Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#447 ⋊ C2 |
| Sylow | C11 ⋊ #3008 |
784 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^d=h^10127 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3008, C2×#13077879, #15620236, … |
| maximal normal subgroup of | D11×#3008, C2×#13077879, #15620236, … |
| maximal quotient of | #14726928, #14726934, #14727016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13773);