Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #1417 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^10,c^b=ce,e^b=ef,f^b=fg148 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1417, C2×#13066800, #14674226, … |
| maximal normal subgroup of | D11×#1417, C2×#13066800, #14674226, … |
| maximal quotient of | #14641223, #14641226, #14641334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2694);