Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #2560 |
518 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=fg,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^10178 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2560, C2×#13073756, #14923945, … |
| maximal normal subgroup of | D11×#2560, C2×#13073756, #14923945, … |
| maximal quotient of | #14676133, #14676406, #14677088, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 9650);