Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C89 ⋊ #1569 |
166 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 77 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=d,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,h^b=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36448815, #36448816, #36448822, … |
| maximal normal subgroup of | #36448815, #36448816, #36448822, … |
| maximal quotient of | #36443899, #36445631, #36447269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 3275);