Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1358 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=g,c^2=f,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^10,c^b=cf,d^b=defg,e^b=eg133 conjugacy classes — view the full character table.
| maximal subgroup of | #14641606, #14641607, #14641609, … |
| maximal normal subgroup of | #14641606, #14641607, #14641609, … |
| maximal quotient of | #14640496, #14640506, #14640529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2549);