Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C11×#346 ⋊ C2 |
| Sylow | C11 ⋊ #1330 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^10,c^b=ceg,d^b=dg,h^b=h^10238 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#1330, C2×#13066575, #14663490, … |
| maximal normal subgroup of | D11×#1330, C2×#13066575, #14663490, … |
| maximal quotient of | #14640435, #14640438, #14640441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2469);