Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #1461 |
248 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,89|a^2=e,b^2=f,c^2=fg,e^2=g,b^a=bd,d^a=df,h^a=h^88,e^b=ef1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36441432, #36441433, #36441647, … |
| maximal normal subgroup of | #36441432, #36441433, #36441647, … |
| maximal quotient of | #36442400, #36442406, #36442475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 2834);