Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#131×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2897 |
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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,e^2=g,b^a=be,e^a=eg,h^a=h^88,e^b=eg,h^b=h^88,d^c=dg1804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36570404, #36570408, #36570415, … |
| maximal normal subgroup of | #36570404, #36570408, #36570415, … |
| maximal quotient of | #36520811, #36520907, #36521008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 13037);