Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C82×C11 ⋊ C2 |
| Sylow | C11 ⋊ #1711 |
178 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=dfg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^10358 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1711, C2×#13068228, #14741457, … |
| maximal normal subgroup of | D11×#1711, C2×#13068228, #14741457, … |
| maximal quotient of | #14647552, #14653518, #14653525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4122);