Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C11×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C11 ⋊ #3585 |
1464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^d=h^10151 conjugacy classes — view the full character table.
| maximal subgroup of | #14785060, #14785062, #14785082, … |
| maximal normal subgroup of | #14785060, #14785062, #14785082, … |
| maximal quotient of | #15617341, #15617353, #15617454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 19286);