Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#483 ⋊ C2 |
| Sylow | C11 ⋊ #3326 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^10,c^b=cg,d^b=de,f^c=fg,h^c=h^10,h^d=h^10124 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3326, C2×#13080872, #15630733, … |
| maximal normal subgroup of | D11×#3326, C2×#13080872, #15630733, … |
| maximal quotient of | #14769402, #14770211, #14771010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 16766);