Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C11×#135 ⋊ C2 |
| Sylow | C11 ⋊ #3035 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^10,f^c=fg178 conjugacy classes — view the full character table.
| maximal subgroup of | #14760213, #14760214, #14760224, … |
| maximal normal subgroup of | #14760213, #14760214, #14760224, … |
| maximal quotient of | #14736191, #14736199, #14736206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13961);