Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #462×C89 ⋊ C2 |
| Sylow | C89 ⋊ D4×Q16 |
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^88,e^d=eg,h^d=h^88871 conjugacy classes — view the full character table.
| maximal subgroup of | #36543860, #36543863, #36543868, … |
| maximal normal subgroup of | #36543860, #36543863, #36543868, … |
| maximal quotient of | #36544612, #36544622, #36544627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 16257);