Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #1733 |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^10,c^b=cg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14659092, #14659093, #14659097, … |
| maximal normal subgroup of | #14659092, #14659093, #14659097, … |
| maximal quotient of | #14643211, #14643217, #14643220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4221);