Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C11×#489 ⋊ C2 |
| Sylow | C11 ⋊ #3367 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^10,h^d=h^10109 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#3367, C2×#13081331, #15633583, … |
| maximal normal subgroup of | D11×#3367, C2×#13081331, #15633583, … |
| maximal quotient of | #14770406, #14770595, #14772745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 17225);