Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×B(4,𝔽2) ⋊ C2 |
| Sylow | C11 ⋊ #3025 |
766 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|d^2=g,b^a=be,c^a=cf,f^b=fg,e^c=eg,h^d=h^10112 conjugacy classes — view the full character table.
| maximal subgroup of | #14907791, #14907793, #14907819, … |
| maximal normal subgroup of | #14907791, #14907793, #14907819, … |
| maximal quotient of | #14726038, #14726040, #14726047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13900);