Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #1696 |
140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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=fg,b^2=df,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^88,e^c=eg859 conjugacy classes — view the full character table.
| maximal subgroup of | #1696×D89, C2×#26019778, #36537064, … |
| maximal normal subgroup of | #1696×D89, C2×#26019778, #36537064, … |
| maximal quotient of | #36447525, #36450628, #36450632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 4036);