Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C11 ⋊ #2254 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^10358 conjugacy classes — view the full character table.
| maximal subgroup of | #14641432, #14641434, #14667737, … |
| maximal normal subgroup of | #14641432, #14641434, #14667737, … |
| maximal quotient of | #14670210, #14671808, #14672374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6792);