Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C11×#343 ⋊ C2 |
| Sylow | C11 ⋊ #1822 |
272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^b=h^10,f^c=fg142 conjugacy classes — view the full character table.
| maximal subgroup of | #14664461, #14664463, #14664471, … |
| maximal normal subgroup of | #14664461, #14664463, #14664471, … |
| maximal quotient of | #14647098, #14647101, #14647107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4592);