Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #336×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2093 |
290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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=d,b^2=deg,d^2=g,e^2=g,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,h^b=h^88,d^c=dg,e^c=eg,h^c=h^881792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36443452, #36443472, #36443473, … |
| maximal normal subgroup of | #36443452, #36443472, #36443473, … |
| maximal quotient of | #36459405, #36459444, #36459466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6037);