Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #1385 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,c^2=f,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^10,d^b=dg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14641346, #14641347, #14641349, … |
| maximal normal subgroup of | #14641346, #14641347, #14641349, … |
| maximal quotient of | #14640649, #14640694, #14640819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2614);