Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C11×#117 ⋊ C2 |
| Sylow | C11 ⋊ #1875 |
412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,b^2=dfg,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,h^a=h^10,d^b=dg,f^b=fg238 conjugacy classes — view the full character table.
| maximal subgroup of | #14646101, #14646102, D11×#1875, … |
| maximal normal subgroup of | #14646101, #14646102, D11×#1875, … |
| maximal quotient of | #14648309, #14648324, #14648541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 4832);