Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C11 ⋊ M128 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^10400 conjugacy classes — view the full character table.
| maximal subgroup of | #14641579, #14641580, #14641583, … |
| maximal normal subgroup of | #14641579, #14641580, #14641583, … |
| maximal quotient of | #14641578, C22⋊(C11⋊C64), C4⋊(C11⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2721);