Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #416×C89 ⋊ C2 |
| Sylow | C89 ⋊ #1794 |
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^88,d^b=dg,e^b=eg,d^c=dg,h^c=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1794×D89, C2×#26020217, #36553753, … |
| maximal normal subgroup of | #1794×D89, C2×#26020217, #36553753, … |
| maximal quotient of | #36445828, #36445833, #36445838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4475);