Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C11 ⋊ #2888 |
756 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 289 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^7,11|a^2=f,f^2=g,b^a=be,e^a=eg,h^a=h^10,f^b=fg,d^c=dg211 conjugacy classes — view the full character table.
| maximal subgroup of | #14671337, #14671341, #14671351, … |
| maximal normal subgroup of | #14671337, #14671341, #14671351, … |
| maximal quotient of | #14719592, #14719606, #14719680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12989);