Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C89 ⋊ #3356 |
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^88,c^b=cg,d^b=de,f^c=fg,h^c=h^881261 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36545430, #36545432, #36545445, … |
| maximal normal subgroup of | #36545430, #36545432, #36545445, … |
| maximal quotient of | #36570878, #36570900, #36572186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 17126);