Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#137×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3046 |
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^88,d^b=dg,h^b=h^88,f^c=fg1000 conjugacy classes — view the full character table.
| maximal subgroup of | #36592501, #36592506, #36592516, … |
| maximal normal subgroup of | #36592501, #36592506, #36592516, … |
| maximal quotient of | #36539898, #36539909, #36539920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 14064);