Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1384 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=d,b^2=e,c^2=f,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 | #14641340, #14641341, #14641343, … |
| maximal normal subgroup of | #14641340, #14641341, #14641343, … |
| maximal quotient of | #14640649, #14640697, #14640813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2612);