Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #2472 |
786 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|b^2=f,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^10,c^b=cg,h^b=h^10,h^c=h^10,h^d=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2472, C2×#13072749, #14921559, … |
| maximal normal subgroup of | D11×#2472, C2×#13072749, #14921559, … |
| maximal quotient of | #14675694, #14675927, #14676765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 8643);