Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #2110 |
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,c^b=cg,d^b=dg,h^b=h^10244 conjugacy classes — view the full character table.
| maximal subgroup of | #14668605, #14668607, #14668794, … |
| maximal normal subgroup of | #14668605, #14668607, #14668794, … |
| maximal quotient of | #14662777, #14662779, #14662781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 6114);