Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #3117 |
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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|c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^c=dg,f^c=fg,h^d=h^10127 conjugacy classes — view the full character table.
| maximal subgroup of | #14726365, #14726367, #14726387, … |
| maximal normal subgroup of | #14726365, #14726367, #14726387, … |
| maximal quotient of | #14753833, #14756812, #14756831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 14676);