Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C11×#100 ⋊ C2 |
| Sylow | C11 ⋊ #2019 |
362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^7,11|a^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^10,c^b=cf,d^b=dg,f^b=fg,h^b=h^10,d^c=dg,e^c=eg,f^c=fg136 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#2019, C2×#13069732, #14780975, … |
| maximal normal subgroup of | D11×#2019, C2×#13069732, #14780975, … |
| maximal quotient of | #14654380, #14654397, #14654447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 5626);