Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×C4⋊C8 ⋊ C2 |
| Sylow | C11 ⋊ #2992 |
356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,d^b=dg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14647890, #14647894, #14647897, … |
| maximal normal subgroup of | #14647890, #14647894, #14647897, … |
| maximal quotient of | #14752570, #14752637, #14752715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13646);