Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3168 |
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,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 | #36464411, #36464416, #36464429, … |
| maximal normal subgroup of | #36464411, #36464416, #36464429, … |
| maximal quotient of | #36554973, #36558635, #36558644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 15083);