Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C11×C22⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #2692 |
536 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=e,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^10172 conjugacy classes — view the full character table.
| maximal subgroup of | #14960570, #14960579, #14960644, … |
| maximal normal subgroup of | #14960570, #14960579, #14960644, … |
| maximal quotient of | #14681124, #14681228, #14681556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 11002);