Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #1838 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^10,c^b=cg232 conjugacy classes — view the full character table.
| maximal subgroup of | #14640943, #14648172, #14648173, … |
| maximal normal subgroup of | #14640943, #14648172, #14648173, … |
| maximal quotient of | #14647440, #14647444, #14647447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4651);