Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3361 |
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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=g,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^88,f^c=fg1267 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36544281, #36544290, #36544416, … |
| maximal normal subgroup of | #36544281, #36544290, #36544416, … |
| maximal quotient of | #36571022, #36571240, #36573371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17168);