Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#342 ⋊ C2 |
| Sylow | C11 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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=e,b^2=f,c^2=e,b^a=bd,f^a=fg,d^b=dg,h^c=h^10154 conjugacy classes — view the full character table.
| maximal subgroup of | #14664094, #14664096, #14664099, … |
| maximal normal subgroup of | #14664094, #14664096, #14664099, … |
| maximal quotient of | #14644274, #14644278, #14644282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4297);