Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #2103 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^10,h^c=h^10136 conjugacy classes — view the full character table.
| maximal subgroup of | #14667133, #14667138, #14667144, … |
| maximal normal subgroup of | #14667133, #14667138, #14667144, … |
| maximal quotient of | #14658899, #14658904, #14658909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6091);