Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#568 ⋊ C2 |
| Sylow | C11 ⋊ #2956 |
458 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,e^b=eg,h^b=h^10,d^c=dg214 conjugacy classes — view the full character table.
| maximal subgroup of | #14774635, #14774636, #14774638, … |
| maximal normal subgroup of | #14774635, #14774636, #14774638, … |
| maximal quotient of | #14723207, #14723211, #14723218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13417);