Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C11×C4⋊C4 ⋊ C2 |
| Sylow | C11 ⋊ #1439 |
780 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=g,b^2=d,b^a=bd,c^a=ce,c^b=cf,h^c=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14645575, #14645585, #14645602, … |
| maximal normal subgroup of | #14645575, #14645585, #14645602, … |
| maximal quotient of | #14641694, #14641698, #14641700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2752);