Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #490×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3220 |
420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^88,c^b=ce,d^b=dg,f^c=fg,h^d=h^88730 conjugacy classes — view the full character table.
| maximal subgroup of | #36474833 |
| maximal normal subgroup of | #36474833 |
| maximal quotient of | #36563803, #36564217, #36565031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 15561);