Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #346×C89 ⋊ C2 |
| Sylow | C89 ⋊ C4×M32 |
196 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 113 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=d,b^2=e,d^2=f,f^2=g,c^a=cg,h^b=h^88,h^c=h^881840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36463427, #36463431, #36463435, … |
| maximal normal subgroup of | #36463427, #36463431, #36463435, … |
| maximal quotient of | #36463406, #36463420, #36463453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 6103);