Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C11 ⋊ C2 |
| Sylow | C11 ⋊ #2972 |
500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^10268 conjugacy classes — view the full character table.
| maximal subgroup of | #14723204, #14723206, #14723208, … |
| maximal normal subgroup of | #14723204, #14723206, #14723208, … |
| maximal quotient of | #14752443, #14752501, #14752658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13531);