Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #533×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3131 |
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 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|b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^88,h^b=h^88,h^c=h^881276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36449736, #36449752, #36449754, … |
| maximal normal subgroup of | #36449736, #36449752, #36449754, … |
| maximal quotient of | #36554620, #36557041, #36558064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 14835);