Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C11 ⋊ #2880 |
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 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=f,f^2=g,b^a=be,h^a=h^10,d^c=dg250 conjugacy classes — view the full character table.
| maximal subgroup of | #14650078, #14650082, #14650092, … |
| maximal normal subgroup of | #14650078, #14650082, #14650092, … |
| maximal quotient of | #14719958, #14719968, #14719977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12959);