Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^10,c^b=cg,d^b=dg256 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1401, C2×#13066758, #14673982, … |
| maximal normal subgroup of | D11×#1401, C2×#13066758, #14673982, … |
| maximal quotient of | #14641114, #14641174, D4⋊(C11⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2652);