Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #450×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3114 |
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 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|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^88,d^c=dg,f^c=fg,h^d=h^88868 conjugacy classes — view the full character table.
| maximal subgroup of | #36527011, #36527013, #36527031, … |
| maximal normal subgroup of | #36527011, #36527013, #36527031, … |
| maximal quotient of | #36554474, #36557445, #36557464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 14649);