Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #2123 |
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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=g,c^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^10,c^b=cg,e^b=ef,h^b=h^10,e^d=eg133 conjugacy classes — view the full character table.
| maximal subgroup of | #14669343, #14669346, #14669348, … |
| maximal normal subgroup of | #14669343, #14669346, #14669348, … |
| maximal quotient of | #14662868, #14662953, #14663036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6165);