Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#124×C89 ⋊ C2 |
| Sylow | C89 ⋊ #2684 |
688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 137 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,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^881264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36473396, #36473398, #36473873, … |
| maximal normal subgroup of | #36473396, #36473398, #36473873, … |
| maximal quotient of | #36481711, #36481818, #36482228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 10886);