Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #3461 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,h^a=h^10,c^b=cf244 conjugacy classes — view the full character table.
| maximal subgroup of | #14645186, #14645189, #14645569, … |
| maximal normal subgroup of | #14645186, #14645189, #14645569, … |
| maximal quotient of | #14912468, #14912481, #14912737, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17943);